In △ABC, the coordinates of vertices A and B are A(1,2) and B(−3,−1). For each of the given coordinates of vertex C, is △ABC a right triangle? Select Right Triangle or Not a Right Triangle for each set of coordinates. Right Triangle Not a Right

Question

Right Triangle Not a Right Triangle
C(−3,−2)
C(0,−5)
C(1,−2)

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Answer 1 · 2017-11-01T01:35:04

A Right triangle: #C(0,-5)#
Not right triangles: #C(-3,-2), C(1,-2)#

Distance between #A(1,2)# and #B(-3,-1)# is
#AB=sqrt((1-(-3))^2+(2-(-1))^2)=5#

Then, calculate BC and CA to find if △ABC is a right triangle.

[1] #C(-3,-2)#
#BC=sqrt((-3-(-3))^2+(-2-(-1))^2)=1#
#CA=sqrt((1-(-3))^2+(2-(-2))^2)=4sqrt(2)#

#AB^2=25,BC^2=1,CA^2=32#
#CA^2≠AB^2+BC^2#

This is not a right triangle.

[2] #C(0,-5)#
#BC=sqrt((-3-0)^2+(-1-(-5))^2)=5#
#CA=sqrt((1-0)^2+(2-(-5))^2)=5sqrt(2)#

#AB^2=25,BC^2=25,CA^2=50#
#CA^2=AB^2+BC^2#

This is a right triangle.

[3] #C(1,-2)#
#BC=sqrt((-3-1)^2+(-1-(-2))^2)=sqrt(17)#
#CA=sqrt((1-1)^2+(2-(-2))^2)=4#

#AB^2=25,BC^2=17,CA^2=16#
#AB^2≠BC^2+CA^2#

This is not a right triangle.