To find the distance between points \( A(-3, 5) \) and \( B(7, 2) \), 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, and \( (x_2, y_2) \) are the coordinates of point B.
Substituting the coordinates of points A and B into the formula:
- \( x_1 = -3 \)
- \( y_1 = 5 \)
- \( x_2 = 7 \)
- \( y_2 = 2 \)
Calculating the differences:
\[ x_2 - x_1 = 7 - (-3) = 7 + 3 = 10 \] \[ y_2 - y_1 = 2 - 5 = -3 \]
Now plug these values into the distance formula:
\[ d = \sqrt{(10)^2 + (-3)^2} \] \[ d = \sqrt{100 + 9} \] \[ d = \sqrt{109} \]
Calculating \( \sqrt{109} \):
\[ \sqrt{109} \approx 10.4403 \]
Rounding to the nearest tenth, we get:
\[ d \approx 10.4 \]
Thus, the distance between points A and B is approximately 10.4.