Question

(3, -4) and (5, -2) are two consecutive vertices of a square in which (2, -2) is an interior point. The centre of the square is

• A. (1, 2)
• B. (3, -2)
• C. (0, 2)
• D. (4, -2)

Answer 1

The correct option is B (3, -2)

Slope of AB = 1 and hence AB is inclined at ${45}^{\circ }$ to the x - axis $AB=2\sqrt{2}$
$\therefore$ diagonal AC = 4 and AC is inclined at ${90}^{\circ }$ to the x - axis. Hence, the centre of the square is at E, 2 units above A and its coordinates are (3, -2). A second square possible is $AB{C}_1{D}_1$ on the side of AB opposite to CD but (2,-2) will not be an interior point.