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)![]() ![]() You can put this solution on YOUR website! 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 \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( " \n" ); document.write( " \n" ); document.write( "and the points have \n" ); document.write( " |