The problem asks to find the distance between points $A = (-5, 5)$ and $B = (5, -5)$ using the distance formula:

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

Where:

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

Let me calculate the distance step by step:

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

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

$d = \sqrt{10^2 + (-10)^2}$

$d = \sqrt{100 + 100} = \sqrt{200}$

Now, I'll compute the square root of 200 and round it to the nearest tenth.The distance $d$ between points A and B is approximately 14.1 units when rounded to the nearest tenth.

Would you like more details on any step? Here are some related questions to explore:

1. How is the distance formula derived from the Pythagorean theorem?
2. What is the significance of each term in the distance formula?
3. Can you calculate the distance between two 3D points using a similar formula?
4. How does the concept of distance apply to vectors?
5. How can we verify the result geometrically on the coordinate plane?

Tip: The distance formula can be used to find the length of any straight line between two points in any dimension!