Find the coordinates of the orthocenter of the triangle with the given vertices.

Question

J(-3,-4) , K(-3,4), and L(5,4)

I first found the the slope of the perpendicular to each line segment. Then used the point slope formula and the given coordinates to form 2 equations and then set the two equal to one another. I solved for x and y. I ended up with (-1,6), which did not seem right. I checked with an orthocenter calculator online, and apparently it is (-3,4).

Please guide me step-by-step!

Answer 1

Let me remind you that every triangle has 3 altitudes. Those lines intersect at a point called the orthocenter of the triangle.

If you draw this triangle in a coordinate plane, you will see that it is a right triangle! The right angle is angle JKL. The two ,legs, JK and LK, are also altitudes. They intersect at the triangle's right angle. This implies that the orthocenter is on the right triangle at point K, the vertex of the right angle of the triangle. The coordinates of this vertex K are (-3, 4) give us the answer.

Answer: (-3,4)