Points that are 15 units from the origin

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Question from Paula, a student:

Thank you for reading my question. This is a great service & I sincerely appreciate your help!
Question:
Find the coordinates of any point(s) 15 units away from the origin with an x-coordinate of 9.

I was given the answer: (9,12) and (9,-12), but I do not understand how these numbers were calculated. Thank you for your help!

Hi Paula.

The distance from the origin to any point (x, y) is sqrt(x² + y²). If you aren't convinced, then draw a line from the origin to the point, from the point straight up (or down) to the x-axis and from there to the origin. That is a right triangle and Pythagoras' Theorem should convince you that the hypotenuse, which is the distance from the origin to the point, is sqrt(x² + y²).

You know the distance and you know the value x. This gives you the hypotenuse and one side length and you just need to find the y value. If you do the calculation

15² = 9² + y²

What values of y work?

Cheers,
Stephen La Rocque.

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