To find the distance between two points $A(2, 4)$ and $B(-5, 4)$, we use the distance formula:

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

Where:

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

Substituting the values:

$d = \sqrt{(-5 - 2)^2 + (4 - 4)^2}$ $d = \sqrt{(-7)^2 + 0^2}$ $d = \sqrt{49 + 0} = \sqrt{49} = 7$

So, the distance between points $A$ and $B$ is 7 units.

Would you like more details or have any other questions?

Here are 5 related questions to expand on this:

1. How do you find the midpoint between two points?
2. What is the formula for the slope of a line between two points?
3. Can the distance formula be derived from the Pythagorean theorem?
4. How does the distance formula change in three dimensions?
5. How do you calculate the area of a triangle with given vertex coordinates?

Tip: The distance formula can also be visualized as the length of the hypotenuse of a right triangle formed by the difference in x and y coordinates between two points.