This question is solved using the distance between two points formula, and doing this, we get that the coordinates are: (12,5) and (12,-5).
Distance between two points:
Suppose that we have two points, \((x_1,y_1)\) and \((x_2,y_2)\). The distance between them is given by:
\(D = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)
In this question:
- Origin: Coordinates (0,0).
- Point with a x-coordinate of 12: P(12,y)
13 units away from the origin:
This means that the distance between P and the origin is 13, so:
\(\sqrt{(12-0)^2+(y-0)^2} = 13\)
\((\sqrt{(12-0)^2+(y-0)^2})^2 = 13^2\)
\(12^2 + y^2 = 13^2\)
\(144 + y^2 = 169\)
\(y^2 = 25\)
\(y = \pm \sqrt{25}\)
\(y = \pm 5\)
Thus, the coordinates are: (12,5) and (12,-5).
A similar question is found at https://brainly.com/question/16663263
