Triangle has coordinates #(-4, 3), (-4, 5)#, and #(1,5)#. How do you prove that the triangle is right-angled?

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Answer 1 · 2017-06-02T10:06:13

See the proof below

The points are

#A=(-4,3)#

#B=(-4,5)#

#C=(1,5)#

The lengths of

#AB=2#

#BC=5#

Firstly, we calculate #AC#, assuming that the angle #hat(ABC)# is a right angle

#AC^2=AB^2+BC^2#

#AC^2=4+25=29#

#AC=sqrt29#

Secondly, we calculate #AC# from the coordinates of points #A=(-4,3)#and #C=(1,5)#

#AC=sqrt((-4-1)^2+(3-5)^2)#

#=sqrt(5^2+2^2)#

#=sqrt29#

As the distance, #AB# is the same by #2# methods of calculation.

We conclude, that as

#AC^2=AB^2+BC^2#

the triangle #ABC#, is right angle at #hatB#

#QED#