Solution: A triangle ABC in which Coordinates of A and B are A(1,−1) and B(3,2).
We have to find the third vertex such that △ABC becomes a right triangle.
Let third vertex be (x,y).
As the two lines will be perpendicular, so product of their slopes is -1.
→Slope of AC × Slope of BC = -1
→[tex]\frac{y+1}{x-1}\times\frac{y-2}{x-3}=-1[/tex]
→y²-y-2= -x²+4 x-3
→x²+y²- 4 x -y+1=0
Also , By applying pythagoras theorem,
AC² + BC²=AB²
(x-1)²+(y+1)²+(x-3)²+(y-2)²=13
x²- 2 x +1+y²+2 y+1+x²-6 x+9+y²-4 y+4=13
2 x² +2y² - 8 x - 2 y+2=0
x² +y²- 4 x-y+1=0
As point (3,-1) satisfies the above equation.Also you can find the solution graphically.
