Question

A triangle has corners A, B, and C located at `(1 ,3 )`, `(7 ,9 )`, and `(5 , 8 )`, respectively. What are the endpoints and length of the altitude going through corner C?

Answer 1

Endpoints are `(5, 8)` and `(11/2, 15,2)`
Length `=1/2sqrt2`

Explanation:

Solve for the equation of the lines passing through points A and B and the one passing through point C perpendicular to line AB.

these 2 lines are:`y=x+2` and `y=-x+13`
simultaneous solution gives the point `(11/2, 15/2)`

so that the endpoints of the altitude going to corner C and this point are `(5, 8)` and `(11/2, 15/2)` respectively.

the length`=sqrt((11/2-5)^2+(15/2-8)^2)`

`=1/2sqrt2`