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

To find the distance between the points (1, 2) and (4, 6), you can use the distance formula derived from the Pythagorean theorem. The distance (d) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by:

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

In this case, the coordinates of the points are:

• ( (x_1, y_1) = (1, 2) )
• ( (x_2, y_2) = (4, 6) )

Substituting these values into the distance formula:

1. Calculate the differences: [ x_2 - x_1 = 4 - 1 = 3 ] [ y_2 - y_1 = 6 - 2 = 4 ]

2. Square these differences: [ (x_2 - x_1)^2 = 3^2 = 9 ] \