Question

IF A(4, 3), B(6, -2) and C(a, -3) are the vertices
of a triangle right angled at A, find a​

Answer 1

Answer:

As this is a right angled triangle, using Pythagoras theorem,

AB² + AC² = BC²

With the help of distance formula,

= > ( 4 - 6 )² + ( 3 + 2 )² + ( 4 - a )² + ( 3 + 3 )² = ( 6 - a )² + ( - 2 + 3 )²

= > ( - 2 )² + ( 5 )² + ( 4 - a )² + ( 6 )² = ( 6 - a )² + ( 1) ²

= > 4 + 25 + ( 4 - a )² + 36 = ( 6 - a )² + 1

= > 64 = ( 6 - a )² - ( 4 - a )²

= > 64 = 36 + a² - 12a - 16 - a² + 8a

= > 64 = 20 - 4a

= > a = - 11

Hence the required value of a is - 11