We need to calculate the length of the line segment $PQ$ using the distance formula:

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

Here, the coordinates of $P$ are $(-4, 1)$ and the coordinates of $Q$ are $(4, 5)$. Substituting into the formula:

$d = \sqrt{(4 - (-4))^2 + (5 - 1)^2}$

$d = \sqrt{(4 + 4)^2 + (5 - 1)^2}$

$d = \sqrt{8^2 + 4^2}$

$d = \sqrt{64 + 16}$

$d = \sqrt{80}$

$d = 8.9 \, \text{(rounded to one decimal place)}.$

Thus, the length of $PQ$ is 8.9 units.

Would you like further details or explanations?

Related Questions

1. How is the distance formula derived from the Pythagorean theorem?
2. How can you verify the result using another method?
3. What is the midpoint of the segment $PQ$?
4. How can the slope of the line segment $PQ$ be calculated?
5. What are some applications of the distance formula in real-life problems?

Tip

Always double-check calculations by substituting values back into the equation to confirm accuracy.