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?

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(13198) (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 .

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).

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