The text in the image states:

"Find the distance between the pair of points
$P(38, -24)$ and $Q(13, -19)$"

This is a problem related to finding the distance between two points in a coordinate plane. The formula to calculate the distance $d$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substituting the coordinates $P(38, -24)$ and $Q(13, -19)$ into the formula:

$d = \sqrt{(13 - 38)^2 + (-19 + 24)^2}$ $d = \sqrt{(-25)^2 + (5)^2}$ $d = \sqrt{625 + 25}$ $d = \sqrt{650}$ $d \approx 25.5$

So, the distance between the two points is approximately 25.5 units.

Would you like further details on this calculation or have any questions?

Related questions:

1. How is the distance formula derived?
2. How do we apply the distance formula in 3D space?
3. What other geometric methods can we use to find distances between points?
4. How would this formula change if the points were expressed in polar coordinates?
5. How does this problem relate to the Pythagorean theorem?

Tip:

For accuracy, remember to keep track of signs when calculating the differences between coordinates.