Q5 of 23 Page 230

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.

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


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