To find the distance between each pair of points shown in the images, we will use the distance formula:

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

Analysis of Each Image:

1. First Image:

   • Points: $(-4, -4)$ and $(0, -4)$
   • These points lie on a horizontal line, so the distance is simply the difference in the $x$-coordinates.

2. Second Image:

   • Points: $(-4, -4)$ and $(4, -4)$
   • Again, these points lie on a horizontal line, and the distance is the difference in the $x$-coordinates.

3. Third Image:

   • Points: $(-4, -2)$ and $(2, 2)$
   • These points do not lie on a horizontal or vertical line, so we will use the full distance formula.

Calculations:

1. Distance between $(-4, -4)$ and $(0, -4)$:

$d = \sqrt{(0 - (-4))^2 + (-4 - (-4))^2} = \sqrt{4^2 + 0^2} = \sqrt{16} = 4.0$

2. Distance between $(-4, -4)$ and $(4, -4)$:

$d = \sqrt{(4 - (-4))^2 + (-4 - (-4))^2} = \sqrt{8^2 + 0^2} = \sqrt{64} = 8.0$

3. Distance between $(-4, -2)$ and $(2, 2)$:

$d = \sqrt{(2 - (-4))^2 + (2 - (-2))^2} = \sqrt{6^2 + 4^2} = \sqrt{36 + 16} = \sqrt{52} \approx 7.2$

Final Answers:

1. The distance between $(-4, -4)$ and $(0, -4)$ is 4.0.
2. The distance between $(-4, -4)$ and $(4, -4)$ is 8.0.
3. The distance between $(-4, -2)$ and $(2, 2)$ is 7.2 (rounded to the nearest tenth).

Would you like further details on these calculations or have any questions?

Related Questions:

1. What is the formula for finding the midpoint of a line segment between two points?
2. How do you find the slope of the line passing through two points?
3. Can the distance formula be used in three-dimensional space, and if so, how?
4. How can you determine if three points are collinear using the distance formula?
5. What are the applications of the distance formula in real-world problems?

Tip:

When using the distance formula, ensure the coordinates are correctly substituted and squared to avoid errors.