Question

The vertices of a triangle are A (-1,-4), B (2,-4) and C (2,-1). Use the distance formula and Pythagoras' theorem to show that triangle ABC is an isosceles right-angled triangle

Answer 1

Isosceles triangle

Explanation:

A triangle is a polygon with three sides and three angles. Types of triangles are isosceles, equilateral, scalene and equilateral.

An isosceles triangle is a triangle with two equal sides and two equal angles.

The distance between two points
`(x_1,y_1)\ and\ (x_2,y_2)` on the coordinate plane is given by:

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2 )`

Given a triangle with vertices A(-1,-4), B(2,-4) and C(2,-1). The sides of the triangle is given by:

`AB=√((2-(-1))^2+(-4-(-4))^2)=3\\\\ AC=√((2-(-1))^2+(-1-(-4))^2)=√(18)=3√(2) \\\\BC=√((2-2)^2+(-1-(-4))^2)=3`

Since AB = BC, we can say that the triangle is an isosceles triangle.