Question

The distance between the points $(x,21)$ and $(4,7)$ is $10 \sqrt{2}.$ Find the sum of all possible values of $x.$

Answer 1

the sum of all possible values of x is: 2+6 = 8

Explanation:

Assume the two points in your question are:

• A
  `(x_(1),y_(1))` = (x,21)
• B
  `(x_(2), y_(2))` = (4,7)

=> The distance between the points A(x,21) and B(4,7) is
`10√(2)`

As we know, the distance of two points can be determined by this formula:

`d=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2}`

Apply this formula in this situation to find all possible values of x, we have:

`\sqrt{(4-x)^(2) + (7-21)^(2) }` =
`(10)/(√(2) )`

<=>
`(4-x)^(2) + 196 = 200`

<=>
`(4-x)^(2) = 4`

<=> (4-x) = 2 or (4-x) = -2

<=> x = 2 or x = 6

=> the sum of all possible values of x is: 2+6 = 8