Question

In △ABC , the coordinates of vertices A and B are A(1,2), and B(−3,−1)?

For each of the given coordinates of vertex C, is △ABC a right triangle?

Answer 1

This is a K-12.com Question
Select Right Triangle or Not a Right Triangle for each set of coordinates.

The correct answers are:

C(-3,-2) Not a Right Triangle C(0,-5) Right Triangle C(1,-2) Not a Right Triangle

Answer 2

ABC would be right angle triangle if C(1,-1) or C(-3,2)

Explanation:

In △ABC , the coordinates of vertices A and B are A(1,2), and B(−3,−1)

We need to find the third vertex of triangle ABC.

ABC is a right angle triangle.

A(1,2) and B(-3,-1)

Using A and B, Two possible right angle triangle.

Case 1: If we draw a vertical line at A and horizontal line at B then intersection point of vertical and horizontal would be third vertex of triangle ABC.

Vertical line at A, x=1

Horizontal line at B, y=-1

Vertex C: (1,-1)

Case 2: If we draw a horizontal line at A and vertical line at B then intersection point of vertical and horizontal would be third vertex of triangle ABC.

Vertical line at B, x=-3

Horizontal line at C, y=2

Vertex C: (-3,2)

Thus, ABC would be right angle triangle if C(1,-1) or C(-3,2)

Please see the attachment to see the process graphically.