Question

What is the distance between point (3,2) and line y=1/4x-9

Answer 1

9.94

Explanation:

y =
`(1)/(4)` x - 9

y - 2 = - 4(x - 3)

y = - 4x + 14

- 4x + 14 =
`(1)/(4)` x - 9

16x - 56 = - x + 36

17x = 92

x =
`(92)/(17)`

y = (-4)
`(92)/(17)` + 14 = -
`(368)/(17)` +
`(238)/(17)` = -
`(130)/(17)`

(3, 2) , (
`(92)/(17)` , -
`(130)/(17)` )

d ≈ 9.94396