Question

Find the distance between the points (7, 2) and (6, 10).

Answer 1

`√(65)`

Explanation:

Hi there!

We want to find the distance between the points (7, 2) and (6, 10).

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 the two points needed to find the formula, let's label their values to avoid confusion

`x_1=7\\y_1=2\\x_2=6\\y_2=10`

Now substitute those values into the formula

`√((x_2-x_1)^2+(y_2-y_1)^2)`

`√((6-7)^2+(10-2)^2)`

Now, under the radical, simplify the values in parentheses

`√((-1)^2+(8)^2)`

Now raise the values under the radical

`√(1+64)`

Add the values under the radical together

`√(65)`

It's always good to simplify the radical if possible, but in this case, we can't. So
`√(65)` is the answer.

Hope this helps!