To the nearest tenth, what is the distance between the points (2, 2/3) and (-7, 4)?

To the nearest tenth, what is the distance between the points (2, 2/3) and (-7, 4)?

• A. 9.6
• B. 7.5
• C. 8.1
• D. 10.2

Answer: (A)

To find the distance between the points (2, 2/3) and (-7, 4), we can use the distance formula, which is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \] Here, the coordinates of the two points are: - \( (x_1, y_1) = (2, \frac{2}{3}) \) - \( (x_2, y_2) = (-7, 4) \) Plugging the values into the formula: 1. Calculate \( x_2 - x_1 \): \[ -7 - 2 = -9 \] 2. Square it: \[ (-9)^2 = 81 \] 3. Calculate \( y_2 - y_1 \): \[ 4 - \frac{2}{3} \] To perform the subtraction, convert 4 to a fraction: \[ 4 = \frac{12}{3} \quad \Rightarrow \quad \frac{12}{3} - \frac{

To find the distance between the points (2, 2/3) and (-7, 4), we can use the distance formula, which is given by:

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

Here, the coordinates of the two points are:

• ( (x_1, y_1) = (2, \frac{2}{3}) )

• ( (x_2, y_2) = (-7, 4) )

Plugging the values into the formula:

1. Calculate ( x_2 - x_1 ):

[

-7 - 2 = -9

]

2. Square it:

[

(-9)^2 = 81

]

3. Calculate ( y_2 - y_1 ):

[

4 - \frac{2}{3}

]

To perform the subtraction, convert 4 to a fraction:

[

4 = \frac{12}{3} \quad \Rightarrow \quad \frac{12}{3} - \frac{