To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \) in a Cartesian plane, you can use the distance formula:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Given the points \( A(5, 3) \) and \( B(15, 10) \):
- \( x_1 = 5 \)
- \( y_1 = 3 \)
- \( x_2 = 15 \)
- \( y_2 = 10 \)
Now plug these values into the distance formula:
\[ d = \sqrt{(15 - 5)^2 + (10 - 3)^2} \]
Calculate the differences:
\[ 15 - 5 = 10 \] \[ 10 - 3 = 7 \]
Now, substitute these values back into the formula:
\[ d = \sqrt{(10)^2 + (7)^2} = \sqrt{100 + 49} = \sqrt{149} \]
Next, calculate \( \sqrt{149} \):
\[ \sqrt{149} \approx 12.206 \]
Rounding to the nearest tenth, the distance \( d \) is approximately:
\[ \boxed{12.2} \]