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, -√2) and (√7,0)

Accepted Answer

Hello today we're going to be finding the distance between the two given points. So our first point is zero comma negative square root of five. And our second point is square root of six comma zero. And in order to find the distance between the two points, we're going to use our distance formula which 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 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 values 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 the square root of six minus X one which is zero. That quantity squared plus Y two which is zero minus Y one which is negative square root of five and minus negative square root of five is going to give us plus square root of five. That quantity squared and all we need to do now is to go ahead and simplify. So the square root of 6 0 is going to give us the square root of six and that quantity is squared and we're adding zero plus the square root of five which is going to give us the square root of five. That quantity squared. Now, squaring a square root allows us to cancel the square root. So the square root of six squared is going to give us just six and the square root of five squared is going to give us five. And finally 6-plus 5 gives us the value of 11. So the distance is going to be the square root of 11 and that's going to be our answer. And that means the solution to this problem is going to be C. So I hope this video helps you 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. (0, -√2) and (√7,0)

Key Concepts

Distance Formula

Simplified Radical Form

Rounding Numbers

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