Question

The points A(4,3) , B(-2,y) and C(-1,4) are the vertices of a right angled isosceles triangle

Answer 1

Hey there!

Length of AB =√[(-2-0)²+(a-3)²]=√4+(a-3)²

Length of BC=√1²+(4-a)²=√1+4-a²

Length of CA=√1²+1²=√2

BC²=AC²+AB²

1+(4-a)²=2+4+(a-3)²

1+16+a²-8a=6+a²+9-6a

17+a²-8a=15+a²-6a

2+a²-a²=-6a+8a

2a=2

a=1

hope helped!