If A (5, 3), B (11, −5) and P (12, y)


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


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 $\triangle \mathrm{APC}$ whose co-ordinates are $\mathrm{A}(5,3) ; \mathrm{B}(11,-5)$;


$\mathrm{P}(12, y)$. So clearly the triangle is, right angled at A. So,




Now apply Pythagoras theorem to get,



$100=50+2 y^{2}+34+4 y$

On further simplification we get the quadratic equation as,

$2 y^{2}+4 y-16=0$


$y^{2}+2 y-8=0$

Now solve this equation using factorization method to get,


Therefore, $y=2,-4$

So the answer is (c)

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