HPLEASE HELP! FREE POINTS! Use the coordinates J(7, 8), K(1, 2) and L(5, 2) for △JKL.
The orthocenter for △JKL is at point N. What is KN rounded to the nearest tenth?
Answer choices:
A) 2.7
B) 4.3
C) 6.0
D) 6.3

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Explanation:

Plot points J, K and L on the same xy coordinate system. Connect the points with three segments to form a triangle. Extend segment KL so that a line forms. We'll call this line KL. Draw a perpendicular line through line KL such that the perpendicular line goes through point J. The equation of this new perpendicular line is x = 7. This is one altitude of the triangle.

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Using the coordinates of J(7,8) and K(1,2), you should find the slope is m = 1. Use the slope formula. Afterward, use y = mx+b to find that the y intercept of line JK is b = 1. Therefore line JK has the equation y = x+1.

The slope here is 1, so the perpendicular slope is -1. The equation of the line going through point L, perpendicular to y = x+1, is y = -x+7. Plug in the coordinates of point L to confirm.

I'm skipping a bunch of steps so let me know if you need me to go over how to find these equations.

From here, notice the graphs of y = -x+7 and x = 7 intersect at the point (7,0). This is the orthocenter. The orthocenter is the intersection of the altitude lines. An altitude line is one that goes through a vertex and it is perpendicular to the opposite side.

So point N is located at (7,0)

Check out the diagram below.

Once we know where point N is located, we use the distance formula to get the length of KN.

The distance from K to N is about 6.3 units

This means the length of segment KN is about 6.3 units.