find the coordinate of any point(s) 10 units away from the origin with x-coordinate of 9 Solution Find the coordinates of the points that are 13 units away from the origin and have an x-coordinate equal to 5 Use the Pythagorean theorem. We are looking for a right triangle that has one leg (x-coordinate) with length 5 and has a hypotenuse (distance from the origin) of 13. The other leg (y-coordinate) must then be sqrt(13^2 - 5^2) = sqrt(169-25) = sqrt(144) = 12. But there are two possible legs of length 12 that lie along x = 5; the coordinates are (5, 12) and (5, -12), because the point could lie below the x-axis as well as above .

1. find the coordinate of any point(s) 10 units away from the origin with x-coordinate of 9
Solution
Find the coordinates of the points that are 13 units away from the origin and have an x-
coordinate equal to 5 Use the Pythagorean theorem. We are looking for a right triangle that has
one leg (x-coordinate) with length 5 and has a hypotenuse (distance from the origin) of 13. The
other leg (y-coordinate) must then be sqrt(13^2 - 5^2) = sqrt(169-25) = sqrt(144) = 12. But there
are two possible legs of length 12 that lie along x = 5; the coordinates are (5, 12) and (5, -12),
because the point could lie below the x-axis as well as above