What is the distance between the points (1, 2) and (4, 6)?

To find the distance between two points in a two-dimensional plane, you can use the distance formula, which is derived from the Pythagorean theorem. The distance ( d ) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by the formula:

[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}

]

In this case, the points are (1, 2) and (4, 6). We can identify (x_1 = 1), (y_1 = 2), (x_2 = 4), and (y_2 = 6).

Now, we can calculate the differences in the x and y coordinates:

1. (x_2 - x_1 = 4 - 1 = 3)
2. (y_2 - y_1 = 6 - 2 = 4)

Next, we substitute these values into the distance formula:

[ d = \sqrt{(3)^2 + (4)^2} ]

Calculating the squares