document.write( "Question 812925: Please Help
\n" ); document.write( "Find all the points having an x-coordinate of 3 whose distance from the point (-2, -1) is 13. \n" ); document.write( "

Algebra.Com's Answer #489414 by jsmallt9(3758) $\"\"$ $\"About$

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:
\n" ); document.write( " $\"d+=+sqrt%28%28x%5B2%5D-x%5B1%5D%29%5E2+%2B+%28y%5B2%5D-y%5B1%5D%29%5E2%29\"$

\n" ); document.write( "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:
\n" ); document.write( " $\"13+=+sqrt%28%283-%28-2%29%29%5E2+%2B+%28y%5B2%5D-%28-1%29%29%5E2%29\"$
\n" ); document.write( "We start by simplifying:
\n" ); document.write( " $\"13+=+sqrt%28%283%2B2%29%5E2+%2B+%28y%5B2%5D%2B1%29%5E2%29\"$
\n" ); document.write( " $\"13+=+sqrt%2825+%2B+y%5B2%5D%5E2%2B2y%5B2%5D%2B1%29\"$
\n" ); document.write( " $\"13+=+sqrt%28y%5B2%5D%5E2%2B2y%5B2%5D%2B26%29\"$
\n" ); document.write( "Now we square both sides:
\n" ); document.write( " $\"169+=+y%5B2%5D%5E2%2B2y%5B2%5D%2B26\"$
\n" ); document.write( "This is a quadratic so we want a zero on one side:
\n" ); document.write( " $\"0+=+y%5B2%5D%5E2%2B2y%5B2%5D-143\"$
\n" ); document.write( "Now we factor:
\n" ); document.write( " $\"%28y%5B2%5D%2B13%29%28y%5B2%5D-11%29=0\"$
\n" ); document.write( "From the Zero Product Property:
\n" ); document.write( " $\"y%5B2%5D%2B13+=+0\"$ or $\"y%5B2%5D-11=0\"$
\n" ); document.write( "Solving:
\n" ); document.write( " $\"y%5B2%5D+=+-13\"$ or $\"y%5B2%5D=+11\"$
\n" ); document.write( "So there are two points with an x-coordinate of 3 which are 13 units away from (-2, -1): (3, -13) and (3, 11) \n" ); document.write( "

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