Question

Find the distance between the given points: (2, -2) and (-4, 7)

Answer 1

`3√(13)`

Explanation:

Hi there!

We want to find the distance between the points (2, -2) and (-4, 7).

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 everything needed to find the distance, but let's label the values of the points to avoid any confusion

`x_1=2\\y_1=-2\\x_2=-4\\y_2=7`

Now substitute those values into the formula and solve

`√((x_2-x_1)^2+(y_2-y_1)^2)`

`√((-4-2)^2+(7--2)^2)`

Simplify

`√((-4-2)^2+(7+2)^2)`

`√((-6)^2+(9)^2)`

Square the numbers under the radical

`√(36+81)`

Add the numbers under the radical together

`√(117)`

Simplify the square root

`3√(13)`

Hope this helps!