To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), we can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Given the coordinates for point A as \( A(-6, 3) \) and point B as \( B(6, 6) \), we can substitute these values into the formula:
- \( x_1 = -6 \)
- \( y_1 = 3 \)
- \( x_2 = 6 \)
- \( y_2 = 6 \)
Now, plug these values into the distance formula:
\[ d = \sqrt{(6 - (-6))^2 + (6 - 3)^2} \]
Calculating inside the parentheses first:
\[ d = \sqrt{(6 + 6)^2 + (6 - 3)^2} = \sqrt{(12)^2 + (3)^2} \]
Now calculate the squares:
\[ d = \sqrt{144 + 9} = \sqrt{153} \]
Finally, we approximate \( \sqrt{153} \):
\[ \sqrt{153} \approx 12.37 \]
This value does not exactly match any of the options provided. However, it seems that none of the given choices (A: 15 units, B: 21 units, C: 3 units, D: 225 units) are correct.
So, the distance from A to B is approximately \( 12.37 \) units, and none of the options are accurate.