Question

If $y$ is a positive integer such that the distance between the points $(-6,-1)$ and $(-6,y)$ is $12$ units, then $y$ is equal to

• A. $5$
• B. $8$
• C. $11$
• D. $1$

Answer 1

The correct option is C $11$

The distance between points $(x_1,y_1)$ and $(x_2,y_2)$ is given by

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

$\therefore$ Given, $\sqrt{(-6+6{)}^2+(y+1{)}^2}=12$
$\Rightarrow \sqrt{y^2+2y+1}=12$
$\Rightarrow y^2+2y+1=144$

$\Rightarrow y^2+2y-143=0$
$\Rightarrow y^2+13y-11y-143=0$
$\Rightarrow (y-11)(y+13)=0$

$\Rightarrow y=11$ or $-13$.
The required positive integer is $11$.