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

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

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

`<K = 90°`

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

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