What is the distance between the points (3, 4) and (7, 1) on a coordinate plane?

To determine the distance between the points (3, 4) and (7, 1) on a coordinate plane, we use the distance formula, which is derived from the Pythagorean theorem. The formula for 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 two points are ((x_1, y_1) = (3, 4)) and ((x_2, y_2) = (7, 1)). Plugging these values into the distance formula, we first calculate the differences in the x-coordinates and y-coordinates:

[

x_2 - x_1 = 7 - 3 = 4

]

[

y_2 - y_1 = 1 - 4 = -3

]

Next, we square these differences:

[

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