Question

which points are on the axes 5 units from the origin?

Explanation:

Step1: Recall distance on axes

On the x - axis, a point is of the form $(x,0)$ and on the y - axis, a point is of the form $(0,y)$. The distance of a point $(x,0)$ from the origin $(0,0)$ is $|x|$ and of a point $(0,y)$ from the origin is $|y|$.

Step2: Check x - axis

We want a point 5 units from the origin on the axes. On the x - axis, when $x = 5$ or $x=- 5$, the distance from the origin is 5. Point E has coordinates $(5,0)$ which is 5 units from the origin on the x - axis.

Step3: Check y - axis

On the y - axis, when $y = 5$ or $y=-5$, the distance from the origin is 5. Point P has coordinates $(0, - 5)$ which is 5 units from the origin on the y - axis.

Answer:

E, P