Question

Find the distance between the two points in simplest radical form.(3, -6) and (-1,1)

Answer 1

You have the points:

(3, -6)

(-1, 1)

To find the distance between two point knowing the coordinates (x,y) you can use the next formula:

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

Then:

x1 = 3 y1 = -6

x2 = -1 y2 = 1

`d=\sqrt[]{(-1-3)^2+(1-(-6))^2}`
`d=\sqrt[]{(^{}-4)^2+7^2}`
`d=\sqrt[]{16+49}=\sqrt[]{65}`

To simplify you can factorize the number under the root to know if the number can have a part that has a sqare root, as follow:

As you can see 65 can be writen as (5*13) and as none of those numbers have a perfect square root (whole number) the final answer is:

`d=\sqrt[]{65}`