Full solution

Q. Point

\mathrm{O}

is located at

-2

. Points

\mathrm{P}

and

\mathrm{Q}

are each

5

units away from Point

\mathrm{O}

. Where are P and Q located?

\newline

\mathrm{P}=\square \quad \mathrm{Q}=\square

Identify Given Information: Identify the given information and what is being asked. $\newline$ Point $O$ is located at $-2$ on a number line, and Points $P$ and $Q$ are each $5$ units away from Point $O$ . We need to find the coordinates of Points $P$ and $Q$ .
Determine Possible Locations: Determine the possible locations of Point $P$ . Since Point $P$ is $5$ units away from Point $O$ , it can be either $5$ units to the right or $5$ units to the left of Point $O$ . If Point $O$ is at $-2$ , adding $5$ units to the right gives us $P$ $0$ . Subtracting $5$ units to the left gives us $P$ $2$ .
Assign Coordinates: Determine the possible locations of Point $Q$ . Using the same logic as for Point $P$ , Point $Q$ can also be either $5$ units to the right or $5$ units to the left of Point $O$ . However, since Point $P$ and Point $Q$ are distinct points, they must be on opposite sides of Point $O$ . If we assign Point $P$ to be at $P$ $0$ , then Point $Q$ must be at $P$ $2$ , and vice versa.
Assign Coordinates: Determine the possible locations of Point $Q$ . Using the same logic as for Point $P$ , Point $Q$ can also be either $5$ units to the right or $5$ units to the left of Point $O$ . However, since Point $P$ and Point $Q$ are distinct points, they must be on opposite sides of Point $O$ . If we assign Point $P$ to be at $P$ $0$ , then Point $Q$ must be at $P$ $2$ , and vice versa.Assign the coordinates to Points $P$ and $Q$ . We can choose Point $P$ to be at $P$ $0$ and Point $Q$ to be at $P$ $2$ , or Point $P$ to be at $P$ $2$ and Point $Q$ to be at $P$ $0$ . Both answers are correct as the problem does not specify which point is in which direction.