Question

(-2,1),(5,2)

how do I find the distance between the 2 points in simplified radical form

Answer 1

So the trick here is to use the distance formula.

If you plot the two points on a graph, you can form a right triangle with the distance between the two points being the hypotenuse and the x and y distances between them being the two legs of the triangle.

The fact that it's a triangle tells you that the distance corresponds to the pythagorean theorem, \(a^2 + b^2 = c^2\), where \(c\) is the hypotenuse (the distance between the two points). You can calculate \(a\) and \(b\) by determining the distance along the x axis and y axis between the two points.

In this case, the distance between the two points on the x axis is (5 - -2) = 5 + 2 = 7. You can do the same to find the y distance, then plug into the pythagorean theorem to solve the problem.

Is that enough?