To find the length of $AB$ between the points $A(-1, 5)$ and $B(4, 2)$, we can use the distance formula:

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

Here,

• $x_1 = -1$, $y_1 = 5$ (coordinates of $A$)
• $x_2 = 4$, $y_2 = 2$ (coordinates of $B$)

Substituting the values:

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

$d = \sqrt{25 + 9} = \sqrt{34} \approx 5.831$

The length of $AB$ is approximately 5.83 units to 3 significant figures.

Would you like more details or have any questions?

Here are 5 related questions:

1. How is the distance formula derived from the Pythagorean theorem?
2. What is the importance of significant figures in calculations?
3. Can the distance formula be used for 3D coordinates?
4. What are the common errors to avoid when using the distance formula?
5. How would you calculate the midpoint of line segment $AB$?

Tip: Always double-check your sign handling when working with coordinate points!