Question

If $A(5,3)$, $B(11,-5)$ and $P(12,y)$ are the vertices of a right angled triangle, right angled at P, then $y$ is ______.

• A. $-2,4$
• B. $-2,-4$
• C. $2,-4$
• D. $2,4$

Answer 1

The correct option is A $-2,4$

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

$A{B}^2=\sqrt{(11-5{)}^2+(-5-3{)}^2}=10B{C}^2=\sqrt{(11-12{)}^2+(-5-y{)}^2}=\sqrt{1+(-5-y{)}^2}A{B}^2=100B{C}^2=1+(-5-y{)}^{2}A{C}^2=(5-12{)}^2+(3-y{)}^2=49+(3-y{)}^{2}A{B}^2=A{C}^2+B{C}^{2}100=1+(+5+y{)}^2+49+(3-y{)}^2⟹100=1+25+10y+y^2+49+3-6y+y^2⟹2y^2-4y=16\therefore y=-2,4$