The coordinate of the vertice of triangle SUE is S(-2, -4),U(2, –1) and E(8, -9). Using coordinate geometry, prove that a. triangle SUE is a right triangle. b. triangle SUE is not a isoscele right t

Question

The coordinates of the vertices of triangle SUE are S(-2, -4), U(2, –1) and E(8, -9). Using coordinate geometry, prove that

a. triangle SUE is a right triangle. b. triangle SUE is not an isosceles right tri angle.

Answer 1

Drawing the triangle in the coordinate plane, it would appear that SU and UE meet at right angles.

Compute slope of SU = (-1--4)/(2--2) = 3/4

Compute slope of UE = (-9--1)/(8-2) = -8/6 = 4/3

Since the product of those slopes is -1, then SU and UE are perpendicular and form a right angle, so SUE is a right triangle, US and UE are the legs and SE is the hypotenuse.

To provide it is isosceles, we need to compute the length of the legs US and UE.

US = sqrt((2--2)^2 + (-1--4)^2) = sqrt(25) = 5

UE = sqrt((8-2)^2 + (-9--1)^2) = sqrt(100) = 10

Since the legs are of different lengths then SUE is not an isosceles right triangle.