Depth · one concept from first principles · step 2 of 4
The diagonals of the square meet at the midpoint of O(0, 0) and B(4, 4).
The center is the point every half-turn of the square keeps fixed.
6.G.A.1Draw A DiagramA line through the center splits the square into two half-turn copies; any other line is off by a strip. So l passes through (2, 2).
Instead of measuring areas, ask which point every bisector must share.
6.G.A.1Change Focus Count The ComplementAny line that splits the square's area in half must pass through its center .
A half-turn about the center lays the square back onto itself and carries one piece of a line through the center onto the other, so those two pieces have equal area.
A line that misses the center differs from the parallel line through the center by a strip, and that strip adds area to one side only, so its two pieces cannot be equal.
Line l passes through P(1, 3/2) and (2, 2).
Rise over run between the two known points.
8.F.B.4Convert To AlgebraWrite y=(1/2)x+b and substitute x=2, y=2.
One known point pins down the intercept once the slope is known.
8.F.B.4Convert To AlgebraA shape with a center of symmetry is cut in half by exactly the lines through that center.
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