To find the distance between points A and B in grid 3, we can apply the Pythagorean Theorem. The theorem is expressed as:

$c = \sqrt{a^2 + b^2}$

where:

• $c$ is the distance between points A and B,
• $a$ and $b$ are the horizontal and vertical distances between the points, respectively.

Step-by-step:

1. Coordinates of A and B:

   • Point A appears to be at $(2, 2)$.
   • Point B appears to be at $(9, 8)$.

2. Find the horizontal distance ($a$):

   • The difference in the x-coordinates is $9 - 2 = 7$.

3. Find the vertical distance ($b$):

   • The difference in the y-coordinates is $8 - 2 = 6$.

4. Apply the Pythagorean theorem: $c = \sqrt{7^2 + 6^2} = \sqrt{49 + 36} = \sqrt{85}$ $c \approx 9.2$

Thus, the distance between points A and B is approximately 9.2, which rounds to 9.0 to the nearest tenth.

The correct solution for grid 3 is 9.

Would you like more details or have any further questions?

Here are 5 related questions you might consider:

1. How would you calculate the distance for grid 1?
2. Can you derive the formula for the Pythagorean theorem in different coordinate systems?
3. What happens if the points are aligned horizontally or vertically?
4. How does this change if you're working on a 3D coordinate plane?
5. Can the Pythagorean theorem be used for non-right triangles?

Tip: Always ensure the triangle formed is a right triangle when applying the Pythagorean theorem!