Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-6, -1) and (-9, -6)

Explanation:

Step1: Recall the 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, \( x_1 = -6 \), \( y_1 = -1 \), \( x_2 = -9 \), \( y_2 = -6 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1 = -9 - (-6) = -9 + 6 = -3 \)
\( y_2 - y_1 = -6 - (-1) = -6 + 1 = -5 \)

Then, square these differences:
\( (-3)^2 = 9 \)
\( (-5)^2 = 25 \)

Add the squared differences:
\( 9 + 25 = 34 \)

Take the square root of the sum:
\( d = \sqrt{34} \approx 5.83095 \)

Step3: Round to the nearest tenth

Rounding \( 5.83095 \) to the nearest tenth gives \( 5.8 \).

Answer:

\( 5.8 \)