To find the distance $d$ between two points $A(2, 1)$ and $B(-4, 7)$ on the coordinate plane, we can use the distance formula:

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

Where:

• $(x_1, y_1)$ are the coordinates of point A.
• $(x_2, y_2)$ are the coordinates of point B.

Substituting the coordinates of A and B into the formula:

$d = \sqrt{(-4 - 2)^2 + (7 - 1)^2}$ $d = \sqrt{(-6)^2 + (6)^2}$ $d = \sqrt{36 + 36}$ $d = \sqrt{72}$ $d \approx 8.5$

So, the distance between points A and B is approximately 8.5 units when rounded to the nearest tenth.

Let me know if you'd like further explanation!

Follow-up Questions:

1. What is the general formula for finding the distance between two points?
2. How would you calculate the distance if one of the points is at the origin?
3. Can the distance formula be derived from the Pythagorean theorem? If so, how?
4. How would you calculate the distance between points in three-dimensional space?
5. Why is it important to round the result to the nearest tenth in this context?

Tip:

Always double-check your calculations, especially when squaring negative numbers, as it's a common place where mistakes can happen!