To find the distance between two points \( A(x_1, y_1) \) and \( B(x_2, y_2) \), we can use the distance formula derived from the Pythagorean theorem:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
Given the points \( A(7, 6) \) and \( B(3, 1) \):
- \( x_1 = 7 \)
- \( y_1 = 6 \)
- \( x_2 = 3 \)
- \( y_2 = 1 \)
Now we can substitute these values into the distance formula:
\[ d = \sqrt{(3 - 7)^2 + (1 - 6)^2} \] \[ d = \sqrt{(-4)^2 + (-5)^2} \] \[ d = \sqrt{16 + 25} \] \[ d = \sqrt{41} \]
Now, we can use a calculator to find the value of \( \sqrt{41} \):
\[ \sqrt{41} \approx 6.403124237 \]
Rounding this to the nearest hundredth:
\[ d \approx 6.40 \]
Thus, the distance between the two points \( A(7, 6) \) and \( B(3, 1) \) is approximately 6.40.