Question

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

• A. $9$
• B. $3$
• C. $6$
• D. None of the above

Answer 1

Answer: (B)

$3$

Distance between two point $(x_1,y_1)$ and $(x_2,y_2)$ is given by,

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

${10}^2={(10-2)}^2+(y+3{)}^2$

${(y+3)}^2={10}^2-8^2$

${(y+3)}^2=6^2$

$y+3=\pm 6$

$\therefore y=3ory=-9$