Question

The distance between P(12, 6) and Q is 20 units. If Q is on y-axis, find the coordinates of Q.

Answer 1

Step 1: Use the Distance Formula

`"Distance" = sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`

x₁​ = 12, y₁ = 6

x₂ = 0, y₂ = y

Distance = 20

`20 = sqrt((0 − 12)^2 + (y − 6)^2)`

`20 = sqrt(144 + (y − 6)^2)`

Step 2: Square both sides to eliminate the square root.

400 = 144 + (y − 6)²

(y − 6)² = 400 − 144 = 256

Step 3: Solve for y

y − 6 = ± `sqrt256 = ± 16`

y = 6 + 16 = 22

y = 6 − 16 = −10

The coordinates of point Q are:

(0, 22) or (0, −10)