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To find the distance between points \( P \) and \( Q \), we can use the distance formula:

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

Let's identify the coordinates for points \( P \) and \( Q \) from the graph:

- Point \( P \) is at \( (2, 4) \).
- Point \( Q \) is at \( (8, 12) \).

Now plug these coordinates into the distance formula:

\[
\text{Distance} = \sqrt{(8 - 2)^2 + (12 - 4)^2}
\]

Calculating each part:

1. \( 8 - 2 = 6 \) and \( 6^2 = 36 \)
2. \( 12 - 4 = 8 \) and \( 8^2 = 64 \)

Add these values:

\[
\text{Distance} = \sqrt{36 + 64} = \sqrt{100} = 10
\]

### Answer:
The distance between points \( P \) and \( Q \) is \( 10 \) units.

Would you like further details or explanations?

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Here are 5 related questions to expand understanding:

1. How would the distance change if point \( P \) were moved to a different coordinate?
2. Can the distance formula be used in three-dimensional space, and if so, how?
3. How would you find the midpoint between points \( P \) and \( Q \)?
4. What is the significance of the slope of the line segment between \( P \) and \( Q \)?
5. How can we calculate the distance between two points if we only know their polar coordinates?

**Tip:** When using the distance formula, make sure to double-check each coordinate and simplify carefully to avoid mistakes.

Find the distance between points P and Q on the graph.

Learn how to calculate the distance between points P and Q on a coordinate plane using the distance formula. This problem helps students understand core geometry concepts and apply the Pythagorean theorem to find the distance between two points. Ideal for Grades 7-9 students.

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