Question

ABCD is a parallelogram. The coordinates of A, B and C are (4, 5), (–2, 3) and (–3, –5), then the coordinates of D are

• A. (-3, 3)
• B. (3, -5)
• C. (3, -3)
• D. (5, -3)

Answer 1

The correct option is C (3, -3)

A(4, 5), B(–2, 3) and C(–3, –5) are the vertices of parallelogram.

Let its fourth vertex be D(a, b). Join AC and BD, such that AC and BD intersect at O.



We know that, the diagonals of a parallelogram bisect each other.

Therefore, O is the mid-point of AC and BD both.

Using mid-point formula,

Mid-point of AC $=(\frac{4-3}{2},\frac{5-5}{2})=(\frac{1}{2},0)$

Mid-point of BD $=(\frac{a-2}{2},\frac{b+3}{2})$

$\therefore \frac{a-2}{2}=\frac{1}{2}and\frac{b+3}{2}=0$

$\Rightarrow a-2=1andb+3=0$

$\Rightarrow a=3andb=-3$

So, the coordinates of D are (3, –3).

Hence, the correct answer is option (c).