1. The base of an isosceles triangle JKL has the endpoints J and K. Point K is located at (2,1) and the top of the triangle, point L, is located at (-1,5). Use the distance formula to find the location of point J.

Answer 1

If we have to use the distance formula, then we have

LK = sqrt(9+16) = 5
so, JL also is 5.

The question is, where is J?
Note that since LK = 5, it is the hypotenuse of a right triangle, with legs parallel to the axes. Thus, the base of the triangle is parallel to the x-axis.

So, since the base extends to the left of the line x = -1 the same distance it extends to the right, namely 3,

J = (-4,1)

This problem would have been harder if the triangle had been oriented differently.