Question

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

• A. $y=-9$
• B. Both $\left(a\right)$ and $\left(b\right)$
• C. $y=3$
• D. $y=9$

Answer 1

The correct option is B Both $\left(a\right)$ and $\left(b\right)$

It is given that the distance between $(2,-3)$ and $(10,y)$ is 10.
And distance between the points is given by
$\sqrt{{(x_1-x_2)}^2+{(y_1-y_2)}^2}$
Therefore, $\sqrt{(10-2{)}^2+(y+3{)}^2}=10$
$\sqrt{(8{)}^2+(3+y{)}^2}=10$
$64+(y+3{)}^2=100$
$(y+3{)}^2=36$
$y+3=\pm 6$
$y+3=+6ory+3=-6$
Therefore, $y=3or-9$