How would you prove that the points, (1, -3) and (3,2) and (-2, 4) form the vertices of an isosceles triangle?

Answer 1

(1,-3) vs (3,2)

the distance is sqrt( (3-1)^2 + (2 - -3)^2 ) = sqrt( 4 + 25) = sqrt(29)

(1, -3) vs (-2,4)

the distance is sqrt ( (-2-1)^2 + (4 - -3)^2) = sqrt( 9 + 49) = sqrt(58)

(3,2) vs ( -2,4)

the distance is sqrt ( (3 - -2)^2 + (4 -2)^2) = sqrt( 25 + 4) = sqrt(29)

two sides have measure sqrt(29) while the third side does not.

that makes it an isosceles triangle

Answer 2

In geometry, an isosceles triangle is a triangle that has two sides of equal length.

If the given points are A, B, and C, then use the distance formula. Calculate:

AB

BC

CA

Two of these distances (that is, side lengths) must be equal.

Graphically, if you plot the three points and "connect the dots," it is pretty easy to see which sides are the same length.