In Exercises 1–18, find the distance between each pair of points....

Question

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-2, -6) and (3, −4)

Accepted Answer

Hello. Today we're gonna be finding the distance between the two. Given points. So our first point is negative four comma negative eight. And our second point is five comma negative seven. So in order to find the distance between the two points we need to use the distance formula and the distance formula is the square root of X two minus X one squared plus Y two minus Y one squared. Now in order to get our X one Y one and X two Y two that's going to come directly from the given points. The first point can be labeled as X one comma Y one and the second point can be labeled as X two comma Y two. So all we need to do is go ahead and take these values and plug them into our distance formula. That way we can be able to find the distance. So doing so is going to give us the square root of X two which is five minus x one which is minus negative four. So plus four. That quantity squared plus Y two which is negative seven minus y one which is negative eight and minus negative eight is going to be plus eight. That quantity squared. Now all we need to do is to go ahead and simplify. So five plus four is going to give us nine and that's going to be squared and negative seven plus eight is going to give us one and that's squared nine squared is going to give us 81 1 squared is going to give us one And finally 81 plus one is going to give us 82. So the distance between the two points is going to be the square root of 82, and that's going to be our answer. And the solution to this problem is going to be be so. I hope this video helps you in understanding how to find the distance between two points, and I'll go ahead and see you all in the next video.

In Exercises 1–18, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places. (-2, -6) and (3, −4)

Key Concepts

Distance Formula

Coordinate System

Simplified Radical Form

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