Question

The points (– 4, 0), (4, 0), (0, 3) are the vertices of a ______.

Options

• right triangle

• isosceles triangle

• equilateral triangle

• scalene triangle

Answer 1

The points (– 4, 0), (4, 0), (0, 3) are the vertices of a isosceles triangle.

Explanation:

Let A(– 4, 0), B(4, 0), C(0, 3) are the given vertices.

Now, distance between A(– 4, 0) and B(4, 0),

AB = `sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

AB = `sqrt([4 - (-4)]^2 + (0 - 0)^2` 

= `sqrt((4 + 4)^2`

= `sqrt(8^2)`

= 8

Distance between B(4, 0) and C(0, 3), 

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

= `sqrt(16 + 9)`

= `sqrt(25)`

= 5

Distance between A(– 4, 0) and C(0, 3), 

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

= `sqrt(16 + 9)`

= `sqrt(25)`

= 5

∵ BC = AC

Hence, ΔABC is an isosceles triangle because an isosceles triangle has two sides equal.