Question

Find the value of $a$, if the distance between the points A(-3,-14) and B(a, -5) is 9 units.

• A. 3
• B. -3
• C. $\frac{1}{3}$

Answer 1

The correct option is B -3

According to the question,
Distance between A(-3,-14) and B(a,-5), AB = 9
$\left[\begin{array}{c}\because \text{distance between the points}(x_1,y_1)and(x_2,y_2)\\ =\sqrt{(x_2-x_1{)}^2+(x_2-y_1{)}^2}\end{array}\right]$
$\Rightarrow \sqrt{(a+3{)}^2+(-5+14{)}^2}=9\Rightarrow \sqrt{(a+3{)}^2+(9{)}^2}=9\text{On squaring both the sides, we get}(a+3{)}^2+81=81\Rightarrow (a+3{)}^2=0\Rightarrow a=-3$
Hence, the required value of $a$ is -3.