Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-7,9) and (-2,6)

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, \( x_1=-7,y_1 = 9,x_2=-2,y_2 = 6 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1 \) and \( y_2 - y_1 \):
\( x_2 - x_1=-2-(-7)=-2 + 7 = 5 \)
\( y_2 - y_1=6 - 9=-3 \)

Then, substitute these into the distance formula:
\( d=\sqrt{(5)^2+(-3)^2}=\sqrt{25 + 9}=\sqrt{34} \)

Step3: Calculate the numerical value and round

\( \sqrt{34}\approx5.83095\approx5.8 \) (rounded to the nearest tenth)

Answer:

\( 5.8 \)