Question

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

• A. -9, 3
• B. 9, 3
• C. 9, -3
• D. -9, -3

Answer 1

The correct option is A

-9, 3

Applying distance formula
$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}=d$
$\sqrt{(10-2{)}^2+(y+3{)}^2}=10$
Squaring in both sides
$64+y^2+9+6y=100$
$y^2+6y-27=0$
$y^2+9y-3y-27=0$
$(y+9)(y-3)=0$
$y=-9,3$
The values of y can be 3, -9