A triangle has corners A, B, and C located at (8 ,7 ), (4 ,5 ), and (6 , 2 ), respectively. What are the endpoints and length of the altitude going through corner C?

1 Answer
Jun 21, 2017

The endpoint is =(4.4,5.2)
The length of the altitude is =3.58

Explanation:

The corners of the triangle are

A=(8,7)

B=(4,5)

C=(6,2)

The slope of AB is =(7-5)/(8-4)=2/4=1/2

The slope of the line through C and perpendicular to BC is =-2

The equation of the altitude is

(y-2)=-2(x-6)

y-2=-2x+12

2x+y=14....................(1)

The equation of the line AB is

y-5=1/2(x-4)

2y-10=x-4

2y-x=6......................(2)

Solving for (x,y) in equations (1) and (2), we get the end point of the altitude

2x+((x+6))/2=14

4x+6+x=28

5x=22

x=22/5=4.4

y=14-2*22/5==5.2

The endpoint is =(4.4,5.2)

The length of the altitude is

=sqrt((6-4.4)^2+(2-5.2)^2)

=sqrt(1.6^2+(-3.2)^2)

=sqrt(12.8)

=3.58