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

• A. 3
• B. 4
• C. 5
• D. 6

Answer: (C)

To find the distance between the two points (2, 3) and (5, 7), we use the distance formula, which is derived from the Pythagorean theorem. The distance (d) between two points ((x_1, y_1)) and ((x_2, y_2)) is given by the formula:

[

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

]

Substituting the given points into the formula:

• Here, (x_1 = 2), (y_1 = 3), (x_2 = 5), and (y_2 = 7).

Now, calculate the differences:

• (x_2 - x_1 = 5 - 2 = 3)

• (y_2 - y_1 = 7 - 3 = 4)

Next, substitute these differences into the distance formula:

[

d = \sqrt{(3)^2 + (4)^2}

]

Calculating the squares:

• ((3)^2 = 9)

• \