Triangle ABC has vertices at A(–2, 3), B(–3, –6), and C(2, –1). Is triangle ABC a right triangle? If so, which angle is the right angle?

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geminiprince geminiprince · Answer 1 · 2016-11-14T23:26:30+01:00

no it not its an acute angle

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parmesanchilliwack parmesanchilliwack · Answer 2 · 2019-04-02T08:40:24+02:00

Answer: Yes, ABC is a right triangle.

Step-by-step explanation:

Since, a triangle is called right triangle if the square of one side is equal to the sum of the squares of other two sides.

Here, the vertices of triangle ABC are A(–2, 3), B(–3, –6), and C(2, –1).

By the distance formula,

[tex]AB^2=(-3-(-2))^2+(-6-3)^2[/tex]

[tex]=(-3+2)^2+(-9)^2[/tex]

[tex]=(-1)^2+81=82[/tex]

[tex]BC^2=(2-(-3))^2+(-1-(-6))^2[/tex]

[tex]=(2+3)^2+(-1+6)^2[/tex]

[tex]=5^2+5^2=25+25=50[/tex]

[tex]CA^2=(-2-2)^2+(3-(-1))^2[/tex]

[tex]=(-4)^2+(3+1)^2[/tex]

[tex]=4^2+4^2=32[/tex]

Since,

[tex]AB^2= BC^2+CA^2[/tex]

Hence, ABC is a right angled triangle.