Question

If $A(y,2),$ $B(1,y)$ and $AB=5$, then the possible values of $y$ are

• A. $6,2$
• B. $5,-2$
• C. $-2,-6$
• D. $2,0$

Answer 1

The correct option is B $5,-2$

Distance formula between to points $A(x_1,y_1)$ and $B(x_2,y_2)$ is equal to

$AB=\sqrt{(y_2-y_1{)}^2+(x_2-x_1{)}^2}$

According to the given condition,

$5=\sqrt{(y-2{)}^2+(1-y{)}^2}$

$\Rightarrow 25=y^2+4+y^2+1-4y-2y$

$\Rightarrow 2y^2-6y-20=0$

$\Rightarrow y^2-3y-10=0$

$\Rightarrow y^2-5y+2y-10=0$

$\Rightarrow y(y-5)+2(y-5)=0$

$\Rightarrow y=5,-2$

Hence option $\left(B\right)$ is correct