Question

A triangle has corners A, B, and C located at `(2 ,2 )`, `(3 ,4 )`, and `(6 ,1 )`, respectively. What are the endpoints and length of the altitude going through corner C?

Answer 1

The endpoints `(12/5, 14/5)` and `(6, 1)`
Length `=(9sqrt(5))/5=4.02492`

Explanation:

Solve the equation of the line containing the altitude and that is
`x+2y=8`

Solve the equation of the line containing points A and B and that is
`2x-y=2`

The altitude thru point C has one endpoint at `C(6, 1)` and the other one at `(12/5, 14/5)` obtained by simultaneous solution using the above equations.

The length is `(9sqrt5)/5=4.02492` , computed using distance formula
`d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)`

God bless....I hope the explanation is useful.