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?

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Answer 1 · 2016-12-09T13:31:13

See 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.