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in Geometry and Algebra by (30.8k points)
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In parallelogram ABCD A(x1, y1), B(x3, y2), D(x2, y3) Find the coordinates of C.

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Best answer

Draw AE, DF parallel to x-axis

Draw BE, CF parallel to y-axis

In right triangles ΔAEB, ΔDFE

AB = DC

∠BAE = ∠CDF ∠ABE = ∠DCF

∴ AE = DF = x2 – x1

BE = CF = y2 – y1

x coordinate of C = x3 + DF = x3 + x2 -x,

y coordinate of C = y3 + CF = y3 + y2 – y

∴ C has the coordinates = (x2 + x3 – x1, y2 + y3 – y3)

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