Question

If point A (x, y) B (y , z) and C (z , x) represent vertices of right angled triangle ($\angle B = 90{^\circ}$) then.

• A. x = y
• B. y = z
• C. z =x
• D. x = y = z

Answer 1

Answer: (B)

y = z

Answer 2

$AB^{2} + BC^{2} = AC^{2}$

$(y - x^{2}) + (z - y)^{2} + (z - y)^{2} + (x - z)^{2} = (z - x)^{2} + (x - y)^{2}$

$\Rightarrow 2(z - y)^{2} = 0$

$\Rightarrow z = y$