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. (0, −√3) and (√5, 0)

Accepted Answer

Hello today we're going to be finding the distance between the two given points. So the first point is zero comma negative square root of seven. And the second point is the square root of three comma zero. Now in order to find the distance between the two points, we need to use the distance formula and the distance is equal to the square root of X two minus X one squared plus Y two minus Y one squared. Now in order to get our X two X one Y two and Y one that comes 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. And all we're going to do is just take these individual values and plug them into our distance formula. That way we can find the distance between the two points. So doing so is going to give us the square root of X two which is the square root of three minus X one which is zero. That quantity squared plus Y two which is zero minus Y one which is negative square root of seven and minus negative square root of seven is going to give us positive square root of seven. That quantity squared. And now we need to simplify So square root of 0 is going to give us the square root of three and that's going to be squared and we're adding zero plus the square root of seven which is the square root of seven and that's going to be squared. Now squaring a square root allows us to cancel the square root. So what we are left with is the square root of three squared, which is just three plus the square root of seven squared, which is seven and seven plus three is going to give us 10. So the distance between the two points is going to be the square root of and that's going to be our answer. And the solution to this problem is going to be D. 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.

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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. (0, −√3) and (√5, 0)