Question

Find the distance between the points (2, 7) and (-6, -2).

Answer 1

Approximately 12.04 units.

Explanation:

The find the distance between any two points, we can use the distance formula, which is:

`d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2`

We have the points (2,7) and (-6,-2). Let's let (2,7) be (x₁, y₁) and let's let (-6, -2) be (x₂, y₂). Substitute:

`d=\sqrt{(-6-2)^2+(-2-7)^2`

Subtract:

`d=\sqrt{(-8)^2+(-9)^2`

Square:

`d=√(64+81)`

Add:

`d=√(145)`

Approximate

`d=√(145)\approx12.04`

So, the distance between (2,7) and (-6,-2) is approximately 12.04 units.

And we're done!