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 formula calculates the straight-line distance between two points ((x_1, y_1)) and ((x_2, y_2)) in a two-dimensional space:

[

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

]

Here, ((x_1, y_1) = (3, 4)) and ((x_2, y_2) = (7, 1)).

First, you will find the differences in the x-coordinates and the y-coordinates:

• The difference in the x-coordinates: (x_2 - x_1 = 7 - 3 = 4)

• The difference in the y-coordinates: (y_2 - y_1 = 1 - 4 = -3)

Next, square these differences:

• (4^2 = 16)

• ((-3)^2 = 9)

Now,