What is the distance between the points (3, 4) and (7, 1)?

To find the distance between two points in a Cartesian coordinate system, you can use the distance formula, which is derived from the Pythagorean theorem. The formula is given as:

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

In this case, the points given are (3, 4) and (7, 1). Here, ( (x_1, y_1) ) = (3, 4) and ( (x_2, y_2) ) = (7, 1).

Now, substituting the coordinates into the formula:

1. Calculate the difference in the x-coordinates:

( x_2 - x_1 = 7 - 3 = 4 )

2. Calculate the difference in the y-coordinates:

( y_2 - y_1 = 1 - 4 = -3 )

3. Then square both differences:

( (x_2 - x_1)^2 = 4^2 = 16 )

( (y_2 - y_1)^2 = (-3)^2 = 9