Question 1118318
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The formal algebraic solution method which has you finding the answer by solving a quadratic equation is of course valid.  But the problem can be made much easier than that.<br>
You are looking for the two points on the line x=9 whose distance from (3,-2) is 10.<br>
The horizontal distance from (3,-2) to the line x=9 is 9-3 = 6.  So that horizontal line segment, the line x=9, and the segments from (3,-2) to the points we are looking for will form two right triangles, each with one leg 6 and hypotenuse 10.<br>
Quick use of the Pythagorean Theorem (or the recognition that 6-8-10 is a multiple of the common 3-4-5 right triangle) make the other leg of each right triangle 8.<br>
Then the two points on the line x=9 that are 8 units from y=-2 are -2+8 = 6 and -2 -8 = -10.<br>
So the two points we are looking for are (9,-10) and (9,6).