SOLUTION: The point (x,-1) is 13 units from the point (3,11). What are the possible values of x?

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Question 1137813: The point (x,-1) is 13 units from the point (3,11). What are the possible values of x?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given: The point (x,-1) is 13 units from the point (3,11).
find: What are the possible values of x?


use formula for distance between two points
d=sqrt%28%28x-x%5B1%5D%29%5E2%2B%28y-y%5B1%5D%29%5E2%29
=> given distance d=13, points (x,-1) and (3,11)

13=sqrt%28%28x-3%29%5E2%2B%28-1-11%29%5E2%29
13=sqrt%28%28x-3%29%5E2%2B%28-12%29%5E2%29
13=sqrt%28%28x-3%29%5E2%2B144%29........square both sides
13%5E2=%28sqrt%28%28x-3%29%5E2%2B144%29%29%5E2
169=%28x-3%29%5E2%2B144
169-144=%28x%5E2-6x%2B9%29
25=x%5E2-6x%2B9
0=x%5E2-6x%2B9-25
x%5E2-6x-16=0...factor
x%5E2%2B2x-8x-16=0
%28x%5E2%2B2x%29-%288x%2B16%29=0
x%28x%2B2%29-8%28x%2B2%29=0
%28x-8%29%28x%2B2%29=0
solutions:
x=8 or x=-2-> the possible values of x

so, your point are: (8,-1) and (-2,-1)

check the distance between:
(8,-1) and (3,11)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%283-%288%29%29%5E2%29%2B%28%2811-%28-1%29%29%5E2%29%29
sqrt%28-5%5E2%2B12%5E2%29 The distance is 13.



(-2,-1) and (3,11)
Solved by pluggable solver: Distance Between 2 points
The distance formula is sqrt%28%28%28x%5B2%5D-x%5B1%5D%29%5E2%29%2B%28%28y%5B2%5D-y%5B1%5D%29%5E2%29%29. Plug in the numbers,
sqrt%28%28%283-%28-2%29%29%5E2%29%2B%28%2811-%28-1%29%29%5E2%29%29
sqrt%285%5E2%2B12%5E2%29 The distance is 13.