Question

In △ABC, the coordinates of vertices A and B are A(1,−1) and B(3,2). For each of the given coordinates of vertex C, is △ABC a right triangle?
Select Right Triangle or Not a Right Triangle for each set of coordinates.
C(0,2) right triangle or not a right triangle?
C(3,-1) right triangle or not a right triangle?
C(0,4) right triangle or not a right triangle?

Answer 1

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

→$\frac{y+1}{x-1}\times\frac{y-2}{x-3}=-1$

→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.

Answer 2

Answer:

C(0,2) - Not A Right Angle

C(3,-1) - Right Angle

C(0,4) - Right Angle

I took the unit test and after this was the correct and answer. Hope this helps :))