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Flip across a line creates symmetry · 8 practice problems

4.G.A.3

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Generated variants — 8

Freshly produced from the archetype’s parameters — problem, figure, and solution derived together.

Variant 1 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (3, 5) maps to (1, 3).

(3,5) \to (1,3)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Variant 2 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (3, 5) maps to (1, 3).

(3,5) \to (1,3)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Variant 3 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (3, 7) maps to (1, 5).

(3,7) \to (1,5)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Variant 4 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (3, 6) maps to (2, 5).

(3,6) \to (2,5)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Variant 5 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (2, 6) maps to (0, 4).

(2,6) \to (0,4)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Variant 6 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (2, 4) maps to (2, 4).

(2,4) \to (2,4)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Variant 7 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (4, 7) maps to (1, 4).

(4,7) \to (1,4)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Variant 8 medium

Draw the shape that results when the figure is flipped over the dashed line.

A diagonal dashed line (the line of reflection) runs from the lower left to the upper right across the grid, and a figure is drawn below it. Draw the figure flipped across this dashed line.

Your answer (check it yourself)

Show solution

1 · Understandwhat's really being asked

A figure is drawn below a diagonal dashed reflection line that runs from the lower-left to the upper-right of the grid. We must draw the figure flipped (reflected) across that diagonal line.

Givens

A square grid with a diagonal dashed line of reflection from the lower-left corner to the upper-right corner.
An asymmetric figure (an open polyline) drawn below the line.

Unknowns

The position and shape of the figure after reflecting it across the diagonal dashed line.

Constraints

The reflection is across the diagonal dashed line.
Each reflected point is the same perpendicular distance from the line as the original, on the opposite side.

2 · Planchoose the strategy

#1 Draw a Diagram · also uses: #17 Visualize Spatial Relationships

Reflecting across a line is a point-by-point construction: each vertex maps to a mirror point the same distance across the diagonal. Drawing and visualizing the fold places every corner exactly.

3 · Execute3 carry out the plan

1Identify the mirror line

#1 Draw a Diagram 4.G.A.3

The dashed line goes from the lower-left to the upper-right (a 45-degree diagonal). Reflecting across it swaps the two sides.

A diagonal fold line is like folding paper along that crease so the two halves meet.

2Reflect each corner across the diagonal

#17 Visualize Spatial Relationships 4.G.A.3

For this diagonal, reflecting a grid vertex (c, r) gives the mirror vertex by the swap (c, r) -> (n - r, n - c). For example the corner (2, 5) maps to (1, 4).

(2,5) \to (1,4)

Counting equal grid steps to the other side of the fold places each corner precisely.

3Connect the mirrored corners

#1 Draw a Diagram 4.G.A.3

Join the reflected corner points in the same order as the original to draw the flipped figure above the diagonal line.

The original plus its reflection are symmetric about the dashed line.

Answer: The figure reflected across the diagonal dashed line: a congruent copy on the upper-left side, with each vertex (c, r) moved to (n - r, n - c).

4 · Reviewdoes it hold up?

Each reflected corner is the same distance from the dashed line as its original, just on the other side, so the mirror image is congruent to the original.

Another way: Trace the figure on tracing paper and fold along the dashed diagonal; the traced figure lands where the reflection goes.

Standardsmin grade 4

4.G.A.3 Recognize a line of symmetry for a two-dimensional figure — Reflecting a figure across a line so the figure and its image are symmetric about that line.

💡Takeaway. Flipping across a line is just folding along it - mirror every corner the same distance to the other side!

Where next?

← Back to the problem: Flip across a line creates symmetry