Question

Suppose the coordinate of p=2 and PQ=8. Whare are the possible midpoints for PQ?

Answer 1

The midpoint for segment PQ can be calculated as:

`(P+Q)/(2)`

Then, the midpoint of PQ is:

`\frac{2\text{ + Q}}{2}=1+0.5Q`

Additionally, PQ can be calculated as:

`PQ=\left|Q-P\right|`

So:

`\begin{gathered} \left|Q-P\right|=8 \\ \left|Q-2\right|=8 \end{gathered}`

It means that:

`\begin{gathered} Q-2=8\text{ or } \\ 2\text{ - Q = 8} \end{gathered}`

Solving for Q, we get:

Q = 8 + 2 = 10 or Q = 2 - 8 = -6

Finally, replacing these values on the initial equation for the midpoint, we get:

If Q = 10, then:

midpoint = 1 + 0.5(10) = 1 + 5 = 6

If Q = -6, then:

midpoint = 1 + 0.5(-6) = 1 - 3 = -2

The possible midpoints for PQ are 6 and -2