In the picture, ABCD is a square. Prove that for any point on the diagonal BD, the sum of the x and y coordinates is zero.

Question

Philoid · Accepted Answer

Slope of diagonal AC

⇒ Slope of diagonal AC = 1

Since diagonals of a square are perpendicular to each other

Slope of diagonal AC × Slope of diagonal BD = - 1

⇒ Slope of diagonal BD = - 1

Origin (0,0) is a point on the diagonal

Equation of diagonal BD:

y = - x

⇒ x + y = 0

Hence Proved