Question

Find the values of y for which the distance between the points P (2, - 3) and Q (10, y) is 10 units.

• A. 3
• B. 6
• C. -9
• D. -3

Answer 1

Answer: (A), (C)

The correct options are
A

3

C

-9

It is given that the distance between (2, - 3) and (10, y) is 10.

$\because$ Distance between points $(x_1,y_1)$ and$(x_2,y_2)$ is $\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$.
$\therefore$ $\sqrt{(2-10{)}^2+(-3-y{)}^2}=10$
$\Rightarrow \sqrt{(-8{)}^2+(3+y{)}^2}=10$
$\Rightarrow 64+(y+3{)}^2=100$
$\Rightarrow (y+3{)}^2=36$
$\Rightarrow y+3=\pm 6$
$\Rightarrow y+3=+6ory+3=-6$
Therefore, $y=3or-9$