Question

If two adjacent vertices of a parallelogram are (3, 2) and (−1, 0) and the diagonals intersect at
(2, −5), then find the coordinates of the other two vertices.

Answer 1

We use the formula for finding the coordinates of a point. O is midpoint of both AC and BD.
Hope you understand

Answer 2

The ‘coordinates’ of the other two C and D are (1,-12) and (5,-10)

Solution:

The parallelogram, has been drawn, attached below for clear understanding of the question

The two adjacent sides of the given parallelogram are given by (3, 2) and (−1, 0). The sides that are unknown are denoted as C and D

Now to find the ‘coordinates’ of the parallelogram C, we use the midpoint method

$M(2,-5)=\left(\frac{3+X 1}{2}\right),\left(\frac{2+Y 1}{2}\right)$

$C(X1,Y1)=(1,-12)$

Using the same method we find the value of coordinates of D, we get:

$M(2,-5)=\left(\frac{-1+X 1}{2}\right),\left(\frac{0+Y 1}{2}\right)$

$D(X2,Y2)=(5,-10)$

Therefore, the ‘coordinates’ of C and D are (1,-12) and (5,-10) respectively.