Question

What are the coordinates of the orthocenter of △JKL with vertices at J(−4, −1) , K(−4, 8) , and L(2, 8) ?

Answer 1

Answer:

K(-4,8) is the ortho center.

Step-by-step explanation:

In a right angled triangle, The vertex of the right angle is the ortho center.

Here we are given

J(-4,-1), K(-4,8) & L(2,8)

Using distance formula we get

$JK^{2}= (-4+4)^{2}+ (8+1)^{2}=0+81=81$

$KL^{2}= (-4-2)^{2}+ (8+-8)^{2}=36+0=36$

$JL^{2}= (-4-2)^{2}+ (8+1)^{2}=36+81=117$

So we can say that

$JK^2 + KL^2=JL^2$

By converse of pythagorean theorem we get

Hence the Vertex of the right angle is K(-4,8)

K(-4,8) is the ortho center.