Question

How do you find a possible value for a if the points (7,5), (-9,a) has a distance of `d=2sqrt65`?

Answer 1

`a = {3, 7}`

Explanation:

To solve for the value of `a`, we will use the distance formula:

`"distance" = sqrt(("change in x")^2 + ("change in y")^2)`

The change in `x` is the difference between x-coordinates:

`7 - (-9) = 7 + 9 = 16`

The change in `y` is the difference between y-coordinates:

`5 - a`

Now, plug these values into the distance formula:

`"distance" = sqrt(("change in x")^2 + ("change in y")^2)`

`2sqrt(65) = sqrt((16)^2+(5-a)^2)`

Squaring both sides gives:
`260 = (16)^2+(5-a)^2`
`260 = 256 + (5-a)^2`

`4 = (5-a)^2`
`+-2 = 5-a`
`a = 5 +-2`

Therefore, `a` could be either 3 or 7.