Question

Show that the points (4,9,4),(0,11,2) and (1,0,1) are vertices of Right triangle?
​

Answer 1

Answer:

Step-by-step explanation:

Using the distance formula d=  

(x  

2

​

−x  

1

​

)  

2

+(y  

2

​

−y  

1

​

)  

2

 

​

, we get

AB  

2

=(2+3)  

2

+(6+4)  

2

=5  

2

+10  

2

=25+100=125

BC  

2

=(−6,−2)  

2

+(10−6)  

2

=(−8)  

2

+4  

2

=64+16=80

CA  

2

=(−6+3)  

2

+(10+4)  

2

=(−3)  

2

+(14)  

2

=9+196=205

i.e., AB  

2

+BC  

2

=125+80=205=CA  

2

 

Hence ABC is a right angled triangle since the square of one side is equal to sum of the squares of the other two sides.