Question

If p(5,-2) and R(-5 2) are the coordinates of the opposite vertices of a rectangle PQRS, then the coordinates of the vertex Q and S can be​

Answer 1

Answer:

Equation of line perpendicular to P-

$\frac{y + 2}{x - 5} = - 1 \\ y + 2 = - x + 5 \\ x + y = 3$

Equation of line perpendicular to R-

$\frac{y - 2}{x + 5} = - 1 \\ y - 2 = - x - 5 \\ x + y = - 3$

Also,

$\frac{y + 2}{x - 5} = 1 \\ y + 2 = x - 5 \\ - x + y = - 7$

And

$\frac{y - 2}{x + 5} = 1 \\ y - 2 = x + 5 \\ - x + y = 7$

The coordinates of

Q (2, - 5)

S (-2, 5)