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. (3√3, √5) and (−√3, 4√5)

Accepted Answer

Hello today we're going to be finding the distance between the two given points. So the first point is five square root of two comma square root of three. And our second point is negative square root of two comma two square root of three. Now in order to find the distance between these two points, we're going to use the distance formula. 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 these values, these values are 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 we're going to take these values in the point and directly 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 negative square root of two minus X one which is five square root of two. And that's going to be squared. And we're going to add Y two which is two square root of three minus y one which is square root of three. That quantity squared. Now what we need to do is to go ahead and simplify so negative square root of two minus five. Square root of two is going to give us negative six square root of two. And that quantity is squared and two square root of three minus square root of three is just going to give us the square root of three. That quantity squared now on the side over here, negative six square root of two squared is the same thing as negative. Six square root of two times negative six square root of two, negative six times negative six is going to give us 36 square root of two times square root of two is just going to give us two. So 36 times two is going to give us 72. So negative six square root of two squared is going to evaluate to 72 And the square root of three squared while squaring a square root cancels out the square root. So what we are left with is three and so we can go ahead and rewrite this as the square root of 75 because plus three gives us 75 the square root of 75 can be rewritten as five times the square root of three. And this is going to be the distance between our two given points. And that means that the answer 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. (3√3, √5) and (−√3, 4√5)