Question

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

Answer 1

Answer:

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