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

Answer:

-1.5

Step-by-step 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):

$x_O=\dfrac{x_J+x_K}{2}=\dfrac{-6+3}{2}=\dfrac{-3}{2}=-1.5\\ \\y_O=\dfrac{y_J+y_K}{2}=\dfrac{2+2}{2}=2$

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.