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1. [~/1 Points]DETAILSLARCAAPCALIFind the distance between the two points_ (-5, -3, 2) , (1, -3, 4)Need Help?ReadllWatchlt2__ [-/1 Points]DETAILSLARCAAPCALCFind the...

Question

1. [~/1 Points]DETAILSLARCAAPCALIFind the distance between the two points_ (-5, -3, 2) , (1, -3, 4)Need Help?ReadllWatchlt2__ [-/1 Points]DETAILSLARCAAPCALCFind the distance between the two points_ (3, -9, 8), (3, -9, 9)Need Help?RadllWachlt

1. [~/1 Points] DETAILS LARCAAPCALI Find the distance between the two points_ (-5, -3, 2) , (1, -3, 4) Need Help? Readll Watchlt 2__ [-/1 Points] DETAILS LARCAAPCALC Find the distance between the two points_ (3, -9, 8), (3, -9, 9) Need Help? Radll Wachlt



Answers

Find the distance between the points. $$ (-3,-1),(2,-1) $$

Were given two points and were asked to find the distance between these points so the points are one half four thirds and to negative one. In order to find the distance between these two points, we're going to apply the formula for distance between any two points in the Cartesian plane. So recall this formula says that the distance between two points, which will call x one why one and x two Why to this is the square root of X one minus X two squared plus why one minus y two squared. Therefore, the distance between the two points one half, four thirds and to negative one. This is the square root of one half minus two squared, plus four thirds minus negative. One squared, which is equal to the square roots of one half minus two, is negative. Three halves squared, plus four thirds minus negative. One is seven thirds squared, and this is the square root of 9/4 plus 49 nineths, which is find the least common denominator, which is 36. The square root of C nine times nine is 81 plus 49 times four, which is 160 plus 36 1 96 over four times nine, which is 36. This is equal to the square root of 81 plus 196 which is 277 over the square to 36 which is six. And this is the simplest form, so our answer is squared of.

In this question. We are going to use the distance formula to find the distance between two ordered pairs. The ordered pairs are representing points on a graph. So I am using this idea of a skeleton equation. We have written all of the pieces that we need except for leaving a space to fill in our numbers from our problem. So the numbers that are given to us are negative two thirds. Okay, hama, you make that so we can read it. Sorry -2/3, comma three and negative one. Come up by force. Yeah. All right. Okay. Now we're going to substitute into our equation. R X two minus X one is negative one and negative two thirds. Yeah. Our Why? -1 x one is 5. four and 3. Okay, so cleaning this up a little bit, we have the square root of negative one minus negative two thirds which is negative one plus two thirds. Yeah. Mhm. And then we have five force -3. Mhm Was a long time. Okay. I'm gonna do a little computing off to the side here. I'm going to write negative one As -3/3 plus two thirds, negative three plus two on top is negative one. Nominators three. So this ends up being negative 1/3. Don't forget. We still have to square that thing. Okay. 5 4 -3. Yeah. Yeah, I want a denominator to be four. So I'm going to multiply the top and the bottom of this one by four. So I'm going to change this into five force minus 12 fours Which would be negative 7/4. And remember I still have to square that. Hey, we're still finding the distance here, negative one third squared would be won over nine And -7. 4 squared would be 49/16. Yeah. Yeah. Hey, I need to get a common denominator there. So, I am going to multiply the 1/9 By 16/16. And I'm going to multiply the 49 Over 16 x 9/9 so that I end up with the same denominator of Okay, 16 times nine. So I have 17 Over 1 44 was 49 times nine is 4 41 Over 1 44 and that equals 4 41 plus 17 is 4 58 Over 1 44. So this is equal to the square root of 4 58/1 44. Let me check. A 4 58 is a perfect square root. It is not. Yeah. Hey, Okay, looking back, I believe I have an error in that last step and I see it 16 times one is not 17. 16 times one is 16. Let me fix that. It doesn't really help though because 16 plus 4 41 is 4 57 not for 58 And for 50. So we have four, the square root of 457 Over 1 44, we can break that up to be the square root of 457. Over the square root of 1 44, which would be The square root of 457 for 57 is prime, so it's not going to break down, but the square root of 144 is 12. So this would be the distance between the two points. And if we wanted to get a decimal approximation of that, the square root of 457 divided by 12 would be about 1.78 units. And that's a decimal approximation

This problem. We have the distance formula being used. So we are going Teoh Ah, find the distance between negative five, native three and negative nine. Negative. Six. This looks like negative nine minus and negative five. So plus five squared and then it will have plus a negative six minus negative three. So they plus three squared, which equals the square root of negative four square that 16 plus three squared a negative three squared, which is nine. That's gonna equal a square root of 25 which equals five. And then for part B, we have the square root of For the sake of being able to add easier, we're going to turn this into an improper intern. Improper fraction. So it'll be negative, Um, negative for, uh, negative. 5/2 negative five halves minus nine have squared, and that's going to be plus a negative one minus three squared. That gives us a negative 14 over to which is just seven. So seven negative seven squared is 49 and we're gonna add that to a negative four squared, which is 16. When you add that together, that gives you the square root of 65

Okay, so for part A just wants the distance between two points. We have negative fun. Negative three and negative nine Negative six. So, distance pharmacist, The square root of the difference in the excess square. So the differences in my access is for so we're gonna have four square plus the difference in my wives. The difference of the wise from negative three to negative six is three square, which is equal to the square root of 25. And from a distance between those two points is just equal to fire. Okay, For part being, my two points are because the second point is gonna be from nine over to three on the second point would be negative. 2.5. Negative one. And I'm gonna go in. Right. That is negative. Five house. I get it. Won this per sake of in the fractions. Kind of similar. So same same distance formula. So the difference in my exes. So we have 4.5 and negative 2.5. So the difference in those is gonna be seven. I have seven square and their difference in that and the Y values is 43 from negative oneness. A distance of four. That's the distance between these two points is gonna be the square root of 49 plus 16 which is a square to 65 and come. Thank you very much.


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