The image shows a problem asking for the shortest distance between two points $P(4,3)$ and $Q(2,-1)$. The distance formula 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 of $P(4,3)$ and $Q(2,-1)$:

$d = \sqrt{(2 - 4)^2 + (-1 - 3)^2}$ $d = \sqrt{(-2)^2 + (-4)^2}$ $d = \sqrt{4 + 16}$ $d = \sqrt{20} = 2\sqrt{5}$

So, the shortest distance between points $P$ and $Q$ is $2\sqrt{5}$.

Would you like further details or have any questions?

Here are 5 related questions to expand on this:

1. How do you generalize the distance formula to 3D coordinates?
2. What is the midpoint between points $P(4,3)$ and $Q(2,-1)$?
3. How do you calculate the slope of the line passing through points $P$ and $Q$?
4. If point $R$ lies on the line joining $P$ and $Q$, what would be the ratio of distances if $R$ divides $PQ$ internally?
5. How does the Pythagorean theorem relate to the distance formula in a coordinate plane?

Tip: When using the distance formula, always double-check the signs of the differences between coordinates to avoid mistakes.