Question

Which point is 5 units from A (3,−2)?

Options

• (0, 0)

• (−1, 1)

• (1, 0)

• (1, 1)

Answer 1

(−1, 1)

Explanation:

Use the distance formula:

For each point P(x, y) the distance from A(3, −2) is:

`sqrt((x − 3)^2 + (y + 2)^2)​`

(0, 0) = `sqrt((0 − 3)^2 + (0 + 2)^2)`

= `sqrt(9 + 4)`

= `sqrt13 ≠ 5`

(−1, 1) = `sqrt((−1 − 3)^2 + (1 + 2)^2)`

= `sqrt((−4)^2 + 3^2)` 

= `sqrt(16 + 9)`

= `sqrt25` = 5

(1, 0) = `sqrt((1 − 3)^2 + (0 + 2)^2)`

= `sqrt(4 + 4)`

= `sqrt8 ≠ 5`

(1, −1) = `sqrt((1 − 3)^2 + (−1 + 2)^2)`

(1, −1) = `sqrt(4 + 1)`

= `sqrt5 ≠ 5`