Find The Distance Between Each Pair Of Points Using The Distance Formula (-4,7) And (6,2), Can You Help?

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The distance formula finds the horizontal and vertical distances between the points in the plane and then uses the Pythagorean Theorem (a^2 + b^2 = c^2) to compute the length of the line segment connecting the two points, so if the two points you're finding the distance between are (x1,y1) and (x2,y2), the distance (d) looks like:   

D = sqrt{(x2 - x1)^2 + (y2 - y1)^2}.

Using the values from the points given above, you're looking at    

d = sqrt{(6 - -4)^2 + (2 - 7)^2} = sqrt{10^2 + (-5)^2} = sqrt{100 + 25} = sqrt{125}.    

Unless you need a decimal answer for some reason, sqrt(125) is an exact answer and is preferred to using your calculator.  If you like, you can simplify the radical a little by pulling out a factor of sqrt(25):    

Sqrt(125) = sqrt(25 * 5) = sqrt(25)*sqrt(5) = 5*sqrt(5).

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