Question

17.
If A(5. 3), B(11/-5) and P(12, y) are the vertices of a right triangle right angled at P, then y=
1)-2,4
2)-2,4
3)2, -4
4)2, 4
​

Answer 1

−2,4

If A(5,3) ,B(11,-55) and P(12,y) are the vertices of a right angled triangle,then

AB  

2

=  

(11−5)  

2

+(−5−3)  

2

 

​

=10

BC  

2

=  

(11−12)  

2

+(−5−y)  

2

 

​

=  

1+(−5−y)  

2

 

​

 

AB  

2

=100BC  

2

=1+(−5−y)  

2

 

AC  

2

=(5−12)  

2

+(3−y)  

2

=49+(3−y)  

2

 

AB  

2

=AC  

2

+BC  

2

 

100=1+(+5+y)  

2

+49+(3−y)  

2

 

⟹100=1+25+10y+y  

2

+49+3−6y+y  

2

 

⟹2y  

2

−4y=16

∴y=−2,4