A triangle has corners A, B, and C located at (2 ,7 ), (1 ,4 ), and (6 , 3 ), respectively. What are the endpoints and length of the altitude going through corner C?

1 Answer
Dec 9, 2016

See explanation.

Explanation:

Slope of the line joining AB is (7-4)/(2-1) = 3

Hence the slope of the line perpendicular to AB will be -1/3

And since this line passes through c, it's equation will be

x+3y=15

On solving this line with the equation of AB

(3x-y+1=0)

We get y=9/2 and x=7/6 , so the point (7/6, 9/2) is where the altitude through C intersects AB

Now by applying distance formula between this point and C we can find the length of the altitude.

"Length" = sqrt( ( 29/6)^2 + (3/2)^2 )

You can solve this yourself.