Question

If A (5, 3), B (11, −5) and P (12, y) are the vertices of a right triangle right angled at P, then y=

(a) −2, 4

(b) −2, −4

(c) 2, −4

(d) 2, 4

Answer 1

Disclaimer: option (b) and (c) are given to be same in the book. So, we are considering option (b) as −2, −4
instead of −2, 4.

We have a right angled triangle whose co-ordinates are A (5, 3); B (11,−5);

. So clearly the triangle is, right angled at A. So,

Now apply Pythagoras theorem to get,

So,

On further simplification we get the quadratic equation as,

Now solve this equation using factorization method to get,

Therefore,

So the answer is (c)