SOLUTION: Points J (3, 1) and K (– 1, – 3) are two vertices of an isosceles triangle. If L is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L?

Algebra ->  Triangles -> SOLUTION: Points J (3, 1) and K (– 1, – 3) are two vertices of an isosceles triangle. If L is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L?      Log On


   

Question 1118057: Points J (3, 1) and K (– 1, – 3) are two vertices of an isosceles triangle. If L is the third vertex and has a y-coordinate of 6, what is the x-coordinate of L?
Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


A sketch shows that, with the two given vertices, the third vertex L of an isosceles triangle with y coordinate 6 will be in quadrant II:



In an isosceles triangle, the altitude to the base is perpendicular to the base at the midpoint of the base.

The midpoint of the base JK is M(1,-1); the slope of the base is %281-%28-3%29%29%2F%283-%28-1%29%29=4%2F4=1.

Then, since the altitude LM is perpendicular to the base JK, the slope of the altitude LM is -1.

Then the equation of the altitude LM to the base JK, using the known point (1,-1), is y = -x.



The third vertex L is the point on the altitude where y=6; the equation of the altitude tells us the x value of that point is -6.

So the third vertex L is (-6,6).