In parallelogram ABCD, A(3,2), B(8,4) and D(5,7). Find the coordinates of C.
Draw AE, DF parallel to x-axis and BE, CF parallel to y-axis, as shown in the figure above.
Now, in right triangles △ABE and △DCF,
AB = DC
∠BAE = ∠CDF
∠ABE = ∠DCF
Therefore, AE = DF and BE = CF
Hence AE = DF = 8 -3 = 5 and BE = CF = 4 - 2 = 2
Now, x-coordinate of C = 5 + DF = 5 + 5 = 10
y-coordinate of C = 7 + CF = 7 + 2 = 9
Therefore coordinates of C is (10,9).