Question

(2, 7) and (-6, -2) find the distance between each pair of points

Answer 1

`√(145)`

Explanation:

Hi there!

We are given the points (2, 7) and (-6, -2). We want to find the distance between them. To do that, we can use the distance formula

The distance formula is given as
`√((x_2-x_1)^2+(y_2-y_1)^2)`, where
`(x_1, y_1)` and
`(x_2, y_2)` are points

We have 2 points, which is what we need to find the distance, but let's label their values to avoid any confusion

`x_1=2\\y_1=7\\x_2=-6\\y_2=-2`

Now substitute those values into the formula:

`√((x_2-x_1)^2+(y_2-y_1)^2)`

`√((-6-2)^2+(-2-7)^2)`

Simplify the values under the radical:

`√((-8)^2+(-9)^2)`

Raise to the second power:

`√(64+81)`

Add the numbers under the radical together

`√(145)`

The answer can be left as that, as the radical cannot be simplified.

Hope this helps!