What is the distance between the points (2, 3) and (5, 7)?

To determine the distance between the points (2, 3) and (5, 7), we can use the distance formula, which is derived from the Pythagorean theorem. The formula for the 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, we have the points (2, 3) and (5, 7). Assigning these values:

• ( x_1 = 2 )

• ( y_1 = 3 )

• ( x_2 = 5 )

• ( y_2 = 7 )

Now, we can plug these values into the formula:

1. Calculate ( x_2 - x_1 ):

[

5 - 2 = 3

]

2. Calculate ( y_2 - y_1 ):

[

7 - 3 = 4

]

3. Substitute these values