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

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 points (2, 3) and (5, 7), we apply the distance formula, which is defined as: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] In this scenario, the coordinates of the first point are \((x_1, y_1) = (2, 3)\) and the second point are \((x_2, y_2) = (5, 7)\). Substituting these values into the formula gives us: 1. Calculate the change in the x-coordinates: \[ x_2 - x_1 = 5 - 2 = 3 \] 2. Calculate the change in the y-coordinates: \[ y_2 - y_1 = 7 - 3 = 4 \] 3. Now, substitute these results back into the distance formula: \[ d = \sqrt{(3)^2 + (4)^2} \] 4. Calculate the squares: \[ d = \sqrt{9 + 16} \] 5. Add the squared

To find the distance between the points (2, 3) and (5, 7), we apply the distance formula, which is defined as:

[

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

]

In this scenario, the coordinates of the first point are ((x_1, y_1) = (2, 3)) and the second point are ((x_2, y_2) = (5, 7)).

Substituting these values into the formula gives us:

1. Calculate the change in the x-coordinates:

[

x_2 - x_1 = 5 - 2 = 3

]

2. Calculate the change in the y-coordinates:

[

y_2 - y_1 = 7 - 3 = 4

]

3. Now, substitute these results back into the distance formula:

[

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

]

4. Calculate the squares:

[

d = \sqrt{9 + 16}

]

5. Add the squared