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