Question

In parallelogram ABCD, A(-5,2), B(1,3) and D(-2,10). Then the coordinates of C is

• A. (4,10)
• B. (4,11)
• C. (1,10)
• D. (1,11)

Answer 1

The correct option is B

(4,11)

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 = 1 - (-5) = 6 and BE = CF = 3 - 2 = 1

Now, $x$-coordinate of C = -2 + DF = -2 + 6 = 4

$y$-coordinate of C = 10 + CF = 10 + 1 = 11

Therefore coordinates of C is (4,11).