## Question

###### 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?

## Answers

Endpoints of altitude are

#(59/17,104/17), (1,2)#

Length of altitude#=sqrt(392/17)~~4.802# ## Explanation:

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 = (4-7)/(7-2)=-3/5#

equation of line#AB# is :#y-4=-3/5(x-7)#

#=> 5y=-3x+41# ..... (1)Let slope of line

#AB# be#s_1# , and slope of line#CD# be#s_2#

As line#CD# is perpendicular to line#AB# ,#=> s_1*s_2=-1#

#=> -3/5*s_2=-1, => s_2=5/3#

So slope of line#CD= 5/3#

equation of line#CD# is :#(y-2)=5/3(x-1)#

#=> 3y=5x+1# ..... (2)Solving (1) and (2) we get

#x=59/17, y=104/17#

Hence, endpoints of the altitude are#(59/17, 104/17) and (1,2)# length of altitude

#=sqrt((59/17-1)^2+(104/17-2)^2#

#= sqrt(392/17)~~4.802#