Question

The points A(–4, 0), B(4, 0) and C(0, 3) are the vertices of a triangle, which is ______.

Options

• isosceles

• equilateral

• scalene

• right angled

Answer 1

The points A(–4, 0), B(4, 0) and C(0, 3) are the vertices of a triangle, which is isosceles.

Explanation:

Using the distance formula,

`AC = sqrt((0 - (-4))^2 + (3 - 0)^2)` 

= `sqrt(16 + 9)`

= 5

And `BC = sqrt((0 - 4)^2 + (3 - 0)^2)` 

= `sqrt(16 + 9)`

= 5

While `AB = sqrt((4 - (-4))^2 + (0 - 0)^2)`

= 8 

Two sides (AC and BC) are equal, so the triangle is isosceles (not equilateral or scalene). It is also not right-angled since 5² + 5² ≠ 8².