Question

find the distance between the two points rounding to the nearest tenth (if necessary). (7, -7) and (1, 2)

Explanation:

Step1: Recall distance formula

The distance \( d \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \).
Here, \( x_1 = 7 \), \( y_1 = -7 \), \( x_2 = 1 \), \( y_2 = 2 \).

Step2: Substitute values into formula

First, calculate \( x_2 - x_1 = 1 - 7 = -6 \) and \( y_2 - y_1 = 2 - (-7) = 2 + 7 = 9 \).
Then, square these differences: \( (-6)^2 = 36 \) and \( 9^2 = 81 \).

Step3: Sum the squares and take square root

Sum the squares: \( 36 + 81 = 117 \).
Take the square root: \( d = \sqrt{117} \approx 10.8 \) (rounded to the nearest tenth).

Answer:

\( 10.8 \)