The following are true:
- AB ⊥ AC
- The triangle is a right triangle.
- The triangle is an isosceles triangle.
What a triangle is?
A triangle is a shape with 3 sides and angles
TO get the correct options, we will find the measure of the sides AB, BC, and AC using the distance formula:
For the side AB:
[tex]AB = \sqrt{(-5+1)^2+(-1-3)^2}\\AB = \sqrt{16+16}\\AB = \sqrt{32}\\AB = 4\sqrt{2}[/tex]
For the side AC:
[tex]AC = \sqrt{(3+1)^2+(-1-3)^2}\\AC = \sqrt{16+16}\\AC = \sqrt{32}\\AC = 4\sqrt{2}[/tex]
For the side BC:
[tex]BC = \sqrt{(-5-3)^2+(-1+1)^2}\\BC = \sqrt{64+0}\\BC = \sqrt{64}\\BC = 8[/tex]
Since two sides are equal AB = AC, hence the triangle is an isosceles triangle
From the figure, we can see that the angle between AB and AC is 90degrees, hence AB ⊥ AC and the triangle is a right triangle
Learn more on right triangles here: https://brainly.com/question/15739772
