Question

The distance of which of the following points from the origin is less than 5 units?

Options

• (3, 4)

• (2, 6)

• (−3, −4)

• (1, 4)

Answer 1

(1, 4)

Explanation:

Check distance (3, 4) from (0, 0) = `sqrt((3 - 0)^2 + (4 - 0)^2)`

= `sqrt(9 + 16)`

= 5

Check distance (2, 6) from (0, 0) = `sqrt((2 - 0)^2 + (6 - 0)^2)`

= `sqrt(4 + 36)`

= `sqrt40 > 5 `

Check distance (−3, −4) from (0, 0) = `sqrt((-3-0)^2+(-4 -0)^2)`

= `sqrt(9 + 16)`

= 5

Check distance (1, 4) from (0, 0) = `sqrt((1-0)^2 + (4 - 0)^2)`

= `sqrt(1 + 16)`

= `sqrt17 < 5`