Distance between (1, 2) and (4, 6) equals:

To find the distance between two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ **Step 1: Identify the coordinates.** Let $(x_1, y_1) = (1, 2)$ and $(x_2, y_2) = (4, 6)$. **Step 2: Calculate the differences in $x$ and $y$.** - Difference in $x$: $x_2 - x_1 = 4 - 1 = 3$ - Difference in $y$: $y_2 - y_1 = 6 - 2 = 4$ **Step 3: Square the differences.** - $(3)^2 = 9$ - $(4)^2 = 16$ **Step 4: Sum the squares and take the square root.** - Sum: $9 + 16 = 25$ - Distance: $d = \sqrt{25} = 5$ The distance between the points is 5.