SOLUTION: Use the Distance Formula to decide whether PQ = QR. P (4,-4) Q (1,-6) R (-1,-3)

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Question 155793This question is from textbook Mc Dougal Littell Geometry
: Use the Distance Formula to decide whether PQ = QR.
P (4,-4)
Q (1,-6)
R (-1,-3) This question is from textbook Mc Dougal Littell Geometry

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the length of PQ



d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%284-1%29%5E2%2B%28-4--6%29%5E2%29 Plug in x%5B1%5D=4, x%5B2%5D=1, y%5B1%5D=-4, and y%5B2%5D=-6.


d=sqrt%28%283%29%5E2%2B%28-4--6%29%5E2%29 Subtract 1 from 4 to get 3.


d=sqrt%28%283%29%5E2%2B%282%29%5E2%29 Subtract -6 from -4 to get 2.


d=sqrt%289%2B%282%29%5E2%29 Square 3 to get 9.


d=sqrt%289%2B4%29 Square 2 to get 4.


d=sqrt%2813%29 Add 9 to 4 to get 13.


So the length of PQ is sqrt%2813%29 units


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Now let's find the length of QR



d=sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2%2B%28y%5B1%5D-y%5B2%5D%29%5E2%29 Start with the distance formula.


d=sqrt%28%281--1%29%5E2%2B%28-6--3%29%5E2%29 Plug in x%5B1%5D=1, x%5B2%5D=-1, y%5B1%5D=-6, and y%5B2%5D=-3.


d=sqrt%28%282%29%5E2%2B%28-6--3%29%5E2%29 Subtract -1 from 1 to get 2.


d=sqrt%28%282%29%5E2%2B%28-3%29%5E2%29 Subtract -3 from -6 to get -3.


d=sqrt%284%2B%28-3%29%5E2%29 Square 2 to get 4.


d=sqrt%284%2B9%29 Square -3 to get 9.


d=sqrt%2813%29 Add 4 to 9 to get 13.


So the length of QR is d=sqrt%2813%29


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Answer:

Since PQ=sqrt%2813%29 and QR=sqrt%2813%29, this means that PQ=QR