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

To find the distance between the points (3, 4) and (7, 1), we can use the distance formula, which is given by the equation:

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

Here, ( (x_1, y_1) ) is the first point (3, 4), and ( (x_2, y_2) ) is the second point (7, 1).

Plugging in the coordinates:

• ( x_1 = 3, y_1 = 4 )
• ( x_2 = 7, y_2 = 1 )

Now, calculate the differences:

• ( x_2 - x_1 = 7 - 3 = 4 )
• ( y_2 - y_1 = 1 - 4 = -3 )

Next, square these differences:

• ( (x_2 - x_1)^2 = 4^2 = 16 )
• ( (y_2 - y_1)^2 = (-3)^2 = 9 )

Now,