Question

Which expression gives the distance between the points (5, 1) and (9, -6)?

Answer 1

so the distance formula: d = rad (x2 - x1)^2 + (y2 - y1)^2
it doesn't matter what order you do, you just have to make sure it's a y coordinate for y and an x coordinate for x.
rad (9-5)^2 + ((-6)-1)^2
rad 4^2 + (-7)^2
rad 16 + 49
rad 65

Answer 2

`d = √(65)\text{ units}`

Explanation:

Let
`(x_1,x_2)` and
`(y_1, y_2)` be the two points.

We have to find the distance between the two points.

The distance Formula:

`d = √((x_1 - y_1)^2 + (x_2 - y_2)^2)`

Here, we are given
`(x_1,x_2)` = (5,1) and
`(y_1, y_2)` = (9,-6)

Then, the distance between these two points is given by:

`d = √((5 - 9)^2 + (1- (-6))^2)`

`d = √((-4)^2 + (7)^2)`

`d = √(16 + 49)`

`d = √(65)`

Thus, the distance between the given point is
`√(65)\text{ units}`.