Show that (-3, 1) , (3, -1) and (1,3) are the vertices of an isosceles triangle.
We know a triangle is an isosceles if two of the sides are the same. In order to prove two sides are the same, we need to work out the distance between two points by using pythagoras’s theorem.
From looking at the coordinates of the points, the distance between the first and third point is the same as the distance between the second and third point. I know this because the two numbers for the difference in the x coordinates and the difference in the y coordinates are the same.
Distance between first and third point = sqrt[ (-3 - 1)^2 + (1 - 3)^2) ]= sqrt20
Distance between second and third point = sqrt[ (3 - 1)^2 + (-1 - 3)^2 ] = sqrt20