Check whether the points ( -2, 3) , (8,3) ,(6,7) are the vertices of a right triangle

Given coordinetes of triangle A(−2,3),B(8,3) and C(6,7)

AB=  

[8−(−2)]  

2

+(3−3)  

2

​

=  

(10)  

2

+(0)  

2

​

=  

100

​

AC=  

[6−(−2)]  

2

+(7−3)  

2

​

=  

(8)  

2

+(4)  

2

​

=  

64+16

​

=  

80

​

BC=  

(6−8)+[7−(2)]

​

2

=  

(−2)  

2

+(4)  

2

​

=  

4+16

​

=  

20

​

If ABC is a right angled triangle, then square of one side must be equal to sum of suare of other two sides.

AB  

2

=(  

100

​

)  

2

=100

and AC  

2

+BC  

2

=(  

80

​

)  

2

+(  

20

​

)  

2

=100

∴AB  

2

=AC  

2

+BC  

2

thus triangle satisfies the Pythagoras theorem

Hence, the triangle is right angled triangle.

Step-by-step explanation:

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