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. (-1/4, -1/7) and (3/4, 6/7)

Accepted Answer

Hey everyone here are asked to find the distance between the two points negative one third and negative 4/5 and the 10.2 3rd and 2/5. Now the first step here is to recall our distance formula which tells us that distance D is equal to the square root of the quantity of X sub two minus x sub one squared plus the quantity of Y sub two minus Y sub one squared. Next we want to note that our first given coordinate point will be the X. Of one and Y sub one point and then our second given point will be the X sub two and Y sub two point. So now we can plug in our given information to our distance formula. So we have distance D is equal to the square root of the quantity of X sub two which is two thirds minus x sub one which is negative one third all squared plus the quantity of y sub two which is 2/5 minus Y sub one which is negative 4/5 again all squared. And from here we can just start simplifying. So we now have the square root of two thirds minus negative one third is just three thirds which is squared plus fifths minus negative 4/5 is 6/5 which is also squared. And from here first we want to note that three thirds is just equal to one. So we can simplify this further and we have the square root of one squared is just one plus 6/5 squared gives us 36 25th. Now to add these together we have to have a common denominator. So we now have, the square root of one becomes 25 divided by 25 plus 36 divided by 25. And now we can add these two fractions together and we get the square root of 61 divided by 25. Now this can be simplified further. We want to note that 61 doesn't have a perfect square which can be removed, but 25 does have five. So we are left with a simplified answer of the square root of 61, all divided by five, which is our answer here for choice B. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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. (-1/4, -1/7) and (3/4, 6/7)

Key Concepts

Distance Formula

Simplified Radical Form

Rounding Numbers

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