Question

Find the distance between the two points in simplest radical form. (6,6) (3,9)

Answer 1

`3√(2)` units

Explanation:

To find the distance between two points on a graph, we use the distance formula
`d=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2` where
`d` is the distance between points
`(x_1,y_1)` and
`(x_2,y_2)`.

For this problem, we will identify
`(x_1,y_1)\rightarrow(6,6)` and
`(x_2,y_2)\rightarrow(3,9)`:

`d=√((y_2-y_1)^2+(x_2-x_1)^2)\\\\d=√((9-6)^2+(3-6)^2)\\\\d=√((3)^2+(-3)^2)\\\\d=√(9+9)\\\\d=√(18)\\\\d=3√(2)`

Therefore, the distance between
`(6,6)` and
`(3,9)` is
`3√(2)` units