Question

ABC is a right angle triangle and B=90° if the points are A(8,-10) B(7,-3) C(0,P) Find the value P

Answer 1

I think this is correct answer.

Answer 2

Answer:

Given that,

A(8,-10) : B(7,-3) : C(0, P)

We need to find the value of P

By Pythagoras Theorem,

$(hypotenuse) {}^{2} = (perpendicular) {}^{2} + (base) {}^{2}$

Here,

Hypotenuse be the distance of 'AC'

Base be the distance of 'BC'

Perpendicular be the distance of 'AB'

$(ac ) {}^{2} = (ab) {}^{2} + (bc) {}^{2}$

$distance \: formula = \sqrt{(x2 - x1) {}^{2} + (y2 - y1) {}^{2} }$

By Using this Formula,

You can Find the values of AB, BC, AC

and substitute in Pythagoras theorem.

$ab = 5 \sqrt{2 } \\ bc = \sqrt{p {}^{2} + 6p + 58} \: \: \: and \: ac = \sqrt{p {}^{2} + 20p + 164 }$

$( \sqrt{p {}^{2} + 20p + 164} ) {}^{2} = (5 \sqrt{2} ) {}^{2} + ( \sqrt{p {}^{2} + 6p + 58 }$

by simplifying this

you will get

p=-4