A triangle has corners A, B, and C located at #(2 ,3 )#, #(3 ,5 )#, and #(4 , 2 )#, respectively. What are the endpoints and length of the altitude going through corner C?

1 Answer
CW
Dec 25, 2016

endpoints of the altitude are #(2,3) and (4,2)#
length of altitude #=sqrt5#

Explanation:

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Given #A(2,3), B(3,5) and C(4,2)#
#=> AB=sqrt((3-2)^2+(5-3)^2)=sqrt5#
#BC=sqrt((4-3)^2+(2-5)^2)=sqrt10#
#AC=sqrt((4-2)^2+(2-3)^2)=sqrt5#
As #AB^2+AC^2=BC^2#,
#=> DeltaABC# is a right-angle triangle, as shown in the diagram.
So line#AC# is the altitude perpendicular to line#AB# from point #C#
#=># endpoints of altitude #= (2,3), and (4,2)#
#=># length of altitude #=AC=sqrt5#

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