Question

In parallelogram ABCD, A(3,2), B(8,4) and D(5,7). Find the coordinates of C.

5,7 3,2) 8.4 

Answer 1

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

$\angle BAE$ = $\angle CDF$

$\angle ABE$ = $\angle DCF$

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).