Question

If the distance between (4, x) and (-5, 8) is `\sqrt 155`, what is the value of `x`?

Answer 1

`x = 16.6024, -0.6024`

Explanation:

Distance formula
`d = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)`

`d = sqrt ((-5-4)^2 + (8-x)^2) = sqrt 155`

`sqrt(9^2 + (8-x)^2) = sqrt 155`

`81 + (8-x)^2 = 155`

`64 - 16x + x^2 = 74`
`x^2-16x -10 = 0`
`x = (16 +-sqrt(256+40))/2 = (16 +-17.2047)/2`

`x = 16.6024, -0.6024`