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 =

Answer 1

${\blue{\underline{\underline{\bold{\huge{Given:-}}}}}}$

The vertices of a right angled triangle are A( 5,3), B( 11,-5) & P( 12,y).

${\blue{\underline{\underline{\bold{\huge{To Find:-}}}}}}$

▪ The value of y

${\blue{\underline{\underline{\bold{\huge{Solution:-}}}}}}$

AP^2 = (12-5)^2 +(y-3)^2

BP^2 = (12-11)^2 + ( y+5)^2

AB^2 = (11-5)^2 +(-5-3)^2

Using Pythagoras theorem

AB^2 = AP^2 + BP^2

➯ 36+64 = 49 + y^2 -6y +9+1 +y^2 +10y +25

➯ 2y^2 + 4y -16 =0

➯y^2 +2y -8=0

➯ (y+4) (y-2) =0

Hence, y = -4 or 2

${\huge{\mathbb{\pink{Hope \ It's\ Helpful..!!!}}}}$