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 \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \).
Let \( (x_1,y_1)=(-6,-1) \) and \( (x_2,y_2)=(-9,-6) \).

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, substitute these into the distance formula:
\( d=\sqrt{(-3)^2+(-5)^2} \)

Step3: Simplify the expression inside the square root

Calculate \( (-3)^2 = 9 \) and \( (-5)^2 = 25 \):
\( d=\sqrt{9 + 25}=\sqrt{34} \)

Step4: Approximate the square root

\( \sqrt{34}\approx5.83095\)

Step5: Round to the nearest tenth

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

Answer:

\( 5.8 \)