Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-2, 0) and (1, 7)

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, \( x_1=-2,y_1 = 0,x_2 = 1,y_2=7 \).

Step2: Substitute the values into the formula

First, calculate \( x_2 - x_1=1-(-2)=1 + 2=3 \) and \( y_2 - y_1=7 - 0 = 7 \).
Then, substitute these into the formula: \( d=\sqrt{(3)^2+(7)^2}=\sqrt{9 + 49}=\sqrt{58} \).

Step3: Calculate the numerical value

\(\sqrt{58}\approx7.6\) (rounded to the nearest tenth).

Answer:

\( 7.6 \)