document.write( "Question 1063151: Find all the points having an x-coordinate of 9 whose distance from the point (3, -2) is 10. \n" ); document.write( "
Algebra.Com's Answer #678173 by KMST(5328)\"\" \"About 
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We can apply the \"distance formula\"
\n" ); document.write( "to set up and solve a quadratic equation
\n" ); document.write( "that would allow us to find the y-coordinate(s)
\n" ); document.write( "of the point(s) (9,y), at distance 10 from (3,-2), if any.
\n" ); document.write( "That may be what was intended.
\n" ); document.write( "We can also understand and reason more,
\n" ); document.write( "while doing less calculations.
\n" ); document.write( "All the points with an x-coordinate of 9
\n" ); document.write( "are on the vertical line x=9.
\n" ); document.write( "All the points at a distance of 10 from point (3,-2)
\n" ); document.write( "are on the circle of radius 10 centered at (3,-2).
\n" ); document.write( "Since the distance between point (3,-2], with x=3,
\n" ); document.write( "and line x=9 is 9-3=6,
\n" ); document.write( "there will be two points meeting both requirements,
\n" ); document.write( "at the intersection of line and circle.
\n" ); document.write( "Going horizontally from (3,-2) to (9,-2),
\n" ); document.write( "continuing vertically for a distance b to one of those points,
\n" ); document.write( "and returning on a straight line to (3,-2),
\n" ); document.write( "we \"draw\" a right triangle.
\n" ); document.write( "The vertical distance, b, according to the Pythagorean theorem,
\n" ); document.write( "satisfies \"b%5E2%2B6%5E2=10%5E3\" .
\n" ); document.write( "We can solve that to find x.
\n" ); document.write( "We can also realize that the very popular 3-4-5 right triangle,
\n" ); document.write( "with sides measuring 3, 4, and 5,
\n" ); document.write( "is similar to our trisngle wicj has sides measuring
\n" ); document.write( "\"2%2A3=6\" , \"2%2A5=10\" , and
\n" ); document.write( "\"2%2A4=b\" , so \"b=8\" ,
\n" ); document.write( "and the points have
\n" ); document.write( "\"y=-2-8=highlight%28-10%29\" and \"y=-2%2B8=highlight%286%29\" .
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