SOLUTION: Point B has coordinates ​(5​,2​). The​ x-coordinate of point A is −7. The distance between point A and point B is 15 units. What are the possible coordinates of point​

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Question 1189956: Point B has coordinates ​(5​,2​). The​ x-coordinate of point A is −7. The distance between point A and point B is 15 units. What are the possible coordinates of point​ A?



Answer by ikleyn(52887) About Me  (Show Source):
You can put this solution on YOUR website!
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Point B has coordinates ​(5​,2​). The​ x-coordinate of point A is −7.
The distance between point A and point B is 15 units.
What are the possible coordinates of point​ A?
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The difference of x =-coordinates between points A and B is dx = 5 - (-7) = 5 + 7 = 12.


The difference of y-coordinates is unknown; let denote it dy.


Then you have this Pythagorean equation to find dy


    12^2 + (dy)^2 = 15^2,


which gives

    
    (dy)^2 = 15^2 - 12^2 = 225 - 144 = 81


hence, dy = +/- sqrt%2881%29 = +/- 9.


It means that two possible coordinates of point A are  (-7,11)  and  (-7,-7).


    ( 11 = 2 + 9  is one possible y-coordinate;  -7 = 2 - 9  is another possible y-coordinate)

Solved.