geometry
posted by Anonymous .
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.

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 xaxis.
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.