B) Show that the points (1,1), (-1,-1) and ( -root3, root 3 ) are the vertices of an equilateral triangle. ​

Given:

The vertices of a triangle are .

To prove:

The given vertices are the vertices of an equilateral triangle.

Solution:

Distance formula:

Let the vertices of the triangle are . Then, by using the distance formula, we get

Similarly,

And,

Clearly, .

Since all sides of the given triangle are equal, therefore the given vertices are the vertices of an equilateral triangle.

Hence proved.

b.-4 units

all you   do is count how many times you move