Find the distance between the points A(1, 2) and B(4, 6) in the rectangular coordinate system.

Step 1 ：Step 1: Identify the coordinates of the points A and B. Point A has coordinates (1, 2) and point B has coordinates (4, 6).

Step 2 ：Step 2: Use the distance formula to calculate the distance between these two points. The distance formula is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).

Step 3 ：Step 3: Substitute the coordinates of the points into the formula. This gives \(d = \sqrt{(4 - 1)^2 + (6 - 2)^2}\).

Step 4 ：Step 4: Simplify the equation. This gives \(d = \sqrt{3^2 + 4^2}\).

Step 5 ：Step 5: Continue to simplify the equation. This gives \(d = \sqrt{9 + 16}\).

Step 6 ：Step 6: Finally, calculate the square root to get the distance. This gives \(d = \sqrt{25}\).