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Let's solve the two parts of this question.

### Part (a): The distance between P and Q
The distance between two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) can be calculated using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Given:
- \( P(0, 10) \)
- \( Q(0, 8) \)

We substitute these values into the formula:

\[
d = \sqrt{(0 - 0)^2 + (8 - 10)^2} = \sqrt{0 + (-2)^2} = \sqrt{4} = 2
\]

So, the distance between P and Q is **2** units.

### Part (b): The coordinates of the midpoint of the line segment PQ
The midpoint of a line segment between points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \) is given by the formula:

\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

Substitute the values:

\[
M = \left( \frac{0 + 0}{2}, \frac{10 + 8}{2} \right) = (0, 9)
\]

So, the midpoint of the line segment PQ is **(0, 9)**.

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Would you like more details or have any questions about the solution? 

Here are 5 related questions to expand on this:
1. How is the distance formula derived from the Pythagorean theorem?
2. What happens if both the x-coordinates and y-coordinates are different for the two points?
3. Can you calculate the slope of the line passing through P and Q?
4. How would you calculate the distance between two points in 3D space?
5. What is the significance of the midpoint in geometric constructions?

**Tip:** Always use parentheses to avoid errors when substituting values into the distance or midpoint formulas.

Find (a) the distance between P and Q and (b) the coordinates of the midpoint of the line segment PQ. P(0,10), Q(0,8)

Solve for the distance and midpoint between points P(0,10) and Q(0,8) using coordinate geometry formulas. This solution covers key concepts such as the distance formula and midpoint formula, suitable for students in Grades 6-8.

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