SOLUTION: Please Help Find all the points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13.

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Question 812925: Please Help
Find all the points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13.
Found 2 solutions by jsmallt9, richwmiller:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Since the problem talks about distance between points in the coordinate plane we will be using the distance formula:
d+=+sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D-y%5B1%5D%29%5E2%29

We are given everything but the y coordinate(s) of the desired points. With only one unknown in the formula we can use it find that unknown:
13+=+sqrt%28%283-%28-2%29%29%5E2+%2B+%28y%5B2%5D-%28-1%29%29%5E2%29
We start by simplifying:
13+=+sqrt%28%283%2B2%29%5E2+%2B+%28y%5B2%5D%2B1%29%5E2%29
13+=+sqrt%2825+%2B+y%5B2%5D%5E2%2B2y%5B2%5D%2B1%29
13+=+sqrt%28y%5B2%5D%5E2%2B2y%5B2%5D%2B26%29
Now we square both sides:
169+=+y%5B2%5D%5E2%2B2y%5B2%5D%2B26
This is a quadratic so we want a zero on one side:
0+=+y%5B2%5D%5E2%2B2y%5B2%5D-143
Now we factor:
%28y%5B2%5D%2B13%29%28y%5B2%5D-11%29=0
From the Zero Product Property:
y%5B2%5D%2B13+=+0 or y%5B2%5D-11=0
Solving:
y%5B2%5D+=+-13 or y%5B2%5D=+11
So there are two points with an x-coordinate of 3 which are 13 units away from (-2, -1): (3, -13) and (3, 11)

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
(-2,-1)
(3,11)
and
(3,-13)