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

To determine the distance between the points (3, 4) and (7, 1), you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula is expressed as:

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

In this case, assign the coordinates of the points as follows:

• ((x_1, y_1) = (3, 4))

• ((x_2, y_2) = (7, 1))

Plugging these values into the formula, you calculate:

1. Find (x_2 - x_1):

(7 - 3 = 4)

2. Find (y_2 - y_1):

(1 - 4 = -3)

3. Square both differences:

((4)^2 = 16)

((-3)^2 = 9)

4. Add the squared differences:

(16 + 9 = 25)

5. Take the square root of the sum:

(\sqrt{25} =