# How do you find all points on the y-axis of a Cartesian coordinate system that are 13 units from (5,0)?

Jan 3, 2017

We are looking for points of the form $\left(0 , y\right)$

#### Explanation:

The distance from the original point is:
${d}^{2} = {\left(\Delta x\right)}^{2} + {\left(\Delta y\right)}^{2}$

${13}^{2} = {\left(5 - 0\right)}^{2} + {\left(0 - y\right)}^{2} = {5}^{2} + {y}^{2} \to$

${y}^{2} = 169 - 25 = 144 \to y = \pm 12$

So the points are $\left(0. + 12\right) \mathmr{and} \left(0 , - 12\right)$