Question

J(–6, 2) and K(3, 2) are the endpoints of the base of an isosceles triangle. Give the x-coordinate of the third vertex.

Answer 1

-1.5

Explanation:

Let L be the third vertex of isosceles triangle JKL.

If JK is the base of this isosceles triangle, then the height drawn from the vertex L divides the base JK into two equal parts.

First, find the coordinates of point O (the midpoint of JK):

`x_O=(x_J+x_K)/(2)=(-6+3)/(2)=(-3)/(2)=-1.5\\ \\y_O=(y_J+y_K)/(2)=(2+2)/(2)=2`

So, O(-1.5, 2)

The third vertex lies on the perpendicular to the base line passing through the point O. This line has the equation x = -1.5. All points lying on this line have x-coordinate of -1.5, thus, the answer is -1.5.