Question

In parallelogram ABCD A(2, 3); B(6, 5); and D(4, 7). Find the coordinates of C

Answer 1

Draw AE, DF parallel to x-axis.

Draw BE, CF parallel to y-axis.

In right triangles Δ ABE, Δ DCF

AB = DC, ∠BAE = ∠CDF

∠ABE = ∠DCF

∴ AE = DF= 6 – 2 = 4

BE = CF = 5 – 3 = 2

x coordinate of C = 4 + DF = 4 + 4 = 8

y coordinate of C = 7 + CF = 7 + 2 = 9

Coordinates ofC (8, 9)