Question

Show that points A(3,-2), B(2,5) and C(-1,1) are vertices of an isosceles triangle?

Answer 1

To proove, that the triangle is isosceles you have tio calculate the length of its sides.

Explanation:

To calculate the length you should use the formula for distance between 2 points on a plane:

`|AB|=sqrt((x_B-x_A)^2+(y_B-y_A)^2)`

If you calculate the sides you will find that:

`|AB|=sqrt((2-3)^2+(5-(-2))^2)=sqrt((-1)^2+7^2)=sqrt(50)=5sqrt(2)`

`|BC|=sqrt((-1-2)^2+(1-5)^2)=sqrt((-3)^2+(-4)^2)=5`

`|AC|=sqrt((-1-3)^2+(1+2)^2)=sqrt((-4)^2+3^2)=5`

`|BC|=|AC|` but `|AC|!=|AB|`, so the triangle is isosceles.