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 , $△ABE$ and $△DCF$ are congruent by ASA criterion.
Hence, AE = DF and BE = CF
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)