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
See explanation.
Explanation:
Slope of the line joining AB is
Hence the slope of the line perpendicular to AB will be
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
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.