Question

In parallelogram ABCD, A(1,3), B(5,3) and D(3,8). Then the coordinates of C are

• A. (7,8)
• B. (6,8)
• C. (8,7)
• D. (5,8)

Answer 1

The correct option is A

(7,8)

In the figure, consider $△AED$ and $△BFC$.

AD = BC, DE = CF and $\angle E$= $\angle F$ = ${90}^{\circ }$

Therefore $△AED$ and $△BFC$ are congruent to each other (by RHS congruence).

So, AE = BF

We see that AE = 3 - 1 = 2 units and so, BF = 2 units.

Also, ED = FC.

Since FC = 8 - 3 = 5 units, we have, ED = 5 units.

$x$-coordinate of C = 5 + BF = 5 + 2 = 7

$y$-coordinate of C = 3 + FC = 3 + 5 = 8

Hence C has the coordinates (7,8).