Question

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

• A. (4,2)
• B. (8,9)
• C. (8,7)
• D. (4,9)

Answer 1

The correct option is B

(8,9)

Draw AE, DF parallel to x-axis.

Draw BE, CF parallel to y-axis.

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 = 6 -2 = 4 and BE = CF = 5 - 3 = 2

Now,
x-coordinate of C = 4 + DF = 4 + 4 = 8
y-coordinate of C = 7 + CF = 7 + 2 = 9

Therefore coordinates of C(8,9)