Question

Find the distance between the two points.

(2,2)

(-3,-4)
Enter the number that
goes beneath the
radical symbol. ✓ [?]

Answer 1

`√(61)`

Explanation:

Hi there!

We are given the points (2, 2) and (-3, -4).

We want to find the distance between them.

We can use the distance formula for that, which is
`√((x_2-x_1)^2+(y_2-y_1)^2)`, where
`(x_1, y_1)` and
`(x_2, y_2)` are points

We have two points, which is needed for that, but let's label their values to avoid confusion

`x_1=2\\y_1=2\\x_2=-3\\y_2=-4`

Now substitute those values into the formula to find the distance

`√((x_2-x_1)^2+(y_2-y_1)^2)`

`√((-3-2)^2+(-4-2)^2)`

Simplify the values under the radical

`√((-5)^2+(-6)^2)`

Raise the numbers under the radical

`√(25+36)`

Add the numbers under the radical together

`√(61)`

The answer cannot be simplified down further, so
`√(61)` is the answer.

Hope this helps!