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?

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.