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Correct answer: A. 5
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.
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