Question

if p(5,2),Q(2,-2) and R(-2,b) are the vertices of a right angled triangle with angle Q=90°, then find b
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Answer 1

Answer:

For the perpendicular condition

$m1 \times m2 = - 1$

So, for PQ

$m1 = \frac{(2 + 2)}{5 - 2} = \frac{4}{3}$

For QR

$m2 = \frac{b + 2}{ - 2 - 2} = \frac{b + 2}{ - 4}$

So,

$\frac{4}{3} \times \frac{b + 2}{ - 4} = - 1 \\ b + 2 = 3 \\ b = 1$