To determine the length of the interval $AB$, we can use the distance formula between two points:

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

where:

• Point $A$ has coordinates $(1, 6)$,
• Point $B$ has coordinates $(7, 2)$.

Let's substitute these coordinates into the formula:

$AB = \sqrt{(7 - 1)^2 + (2 - 6)^2}$ $= \sqrt{6^2 + (-4)^2}$ $= \sqrt{36 + 16}$ $= \sqrt{52}$ $= 7.2 \text{ (to 1 decimal place)}$

So, the length of the interval $AB$ is approximately 7.2.

Would you like further details on the calculation, or do you have any questions?

Here are some related questions to expand understanding:

1. How would you find the length of a line segment between two points in 3D space?
2. What is the general form of the distance formula between two points?
3. How can you verify the accuracy of a calculated distance on a graph?
4. How does the Pythagorean theorem relate to the distance formula?
5. What are some practical applications of calculating distances in coordinate geometry?

Tip: Always double-check your coordinates before substituting them into a formula to avoid errors.