Question

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

Answer 1

B(2, -2), D(-2, 2) are the vertices of the diagonal BD: Sum of x, y coordinates of B = 2 + –2 = 0

Sum of x, y coordinates of D = –2 + 2 = 0

If (x, y)is a point on BD, then

\(\frac{y-2}{x+2}=\frac{2-2}{2+2}\)

\(\frac{y-2}{x+2}=\frac{4}{4}=1\)

y - 2 = -x - 2

y + x = 2 + 2 = 0

x + y = 0