Question

A(0,3),B(-2,y),C(-1,4) is a right angled triangle and right angled at A find the value of y?

Answer 1

given ABC a triangle whose coordinates are A(0,3),B(-2,y),C(-1,4)
Using Pythagoras theorem in right triangle ABC
BC²=AB²+AC²
use distance formula
(-2+1)²+(y-4)²={(-2-0)²+(y-3)²}+{-1-0)²+(4-3)²}
(-1)²+(y²+16-8y)={(-2)²+(y²+9-6y)}+{(-1)²+(1)²}
1+y²+16-8y=4+y²+9-6y+1+1
y²+17-8y=y²+15-6y
y²+17-8y-y²-15+6y=0
-2y+2=0
2=2y
2y=2
y=2/2
y=1
therefore the value of y is 1