Question

EXAMPLE 10 Show that the points (a, a),(-a, - a) and (-3a, 3a) are the vertices of an equilateral triangle. Also find its area.​

Answer 1

The triangle is not equilateral.

Explanation:

Distance formula:

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

Distance from (a, a) to (-a, -a):

`d_1 = √((-a - a)^2 + (-a - a)^2)`

`d_1 = √((-2a)^2 + (-2a)^2)`

`d_1 = √(8a^2)`

Distance from (-a, -a) to (-3a, 3a):

`d_2 = √((-3a - (-a))^2 + (3a - (-a))^2)`

`d_2 = √((-2a)^2 + (4a)^2)`

`d_2 = √(20a^2)`

Distance from (-3a, 3a) to (a, a):

`d_3 = √((-3a - a)^2 + (3a - a)^2)`

`d_3 = √((-4a)^2 + (2a)^2)`

`d_3 = √(20a^2)`

The three sides do not have the same length, so the triangle is not equilateral.