Question

Find the distance between the two points in simplest radical form. (-6,5) and (-3,7)

Answer 1

d =
`√(13)`

Explanation:

The formula for distance, d, between two points is

`d=\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`, where (x1, y1) are one point and (x2, y2) are another point.

We can allow (-6, 5) to be our (x1, y1) point and (-3, 7) to be our (x2, y2) point and plug the points into the formula:

`d=√((-6-(-3))^2+(5-7)^2)\\ d=√((-6+3)^2+(-2)^2)\\ d=√((-3)^2+4)\\ d=√(9+4)\\ d=√(13)`

√13 is already in simplest radical form because there are no perfect squares which can be factored out from 13