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

1 Answer
Feb 11, 2017

Endpoints of altitude are (5917,10417),(1,2)
Length of altitude =392174.802

Explanation:

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As shown in the diagram, line CD is the altitude perpendicular to line AB from point C

Given A(2,7),B(7,4),C(1,2),
slope of line AB=4772=35
equation of line AB is : y4=35(x7)
5y=3x+41 ..... (1)

Let slope of line AB be s1, and slope of line CD be s2
As line CD is perpendicular to line AB, s1s2=1
35s2=1,s2=53
So slope of line CD=53
equation of line CD is : (y2)=53(x1)
3y=5x+1 ..... (2)

Solving (1) and (2) we get x=5917,y=10417
Hence, endpoints of the altitude are (5917,10417)and(1,2)

length of altitude =(59171)2+(104172)2

=392174.802