Question

The vertices of a parallelogram are (2, −3), (6, 5), (-2, 1), (-6, -7) in this order. The point of intersection of the diagonals is

• A. (0, -1)
• B. (0,0)
• C. (-1, 0)
• D. (4,1)

Answer 1

The Correct Option is A

Correct answer: (0, -1) 

Explanation:
In a parallelogram, the diagonals bisect each other. 
So, the point of intersection of the diagonals is the midpoint of both diagonals. Let the vertices of the parallelogram in order be: 
$A(2, -3),\ B(6, 5),\ C(-2, 1),\ D(-6, -7)$ The diagonals are $AC$ and $BD$ Find the midpoint of diagonal $AC$: $$\text{Midpoint of } AC = \left( \frac{2 + (-2)}{2},\ \frac{-3 + 1}{2} \right) = (0, -1)$$ Find the midpoint of diagonal $BD$: $$\text{Midpoint of } BD = \left( \frac{6 + (-6)}{2},\ \frac{5 + (-7)}{2} \right) = (0, -1)$$ Since both diagonals intersect at the same midpoint, the point of intersection is (0, -1).