Question

find the distance between the two points rounding to the nearest tenth (if necessary). (-3, 7) and (-7, 1)

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, \(x_1=-3\), \(y_1 = 7\), \(x_2=-7\), \(y_2=1\).

Step2: Substitute the values into the formula

First, calculate \(x_2 - x_1\) and \(y_2 - y_1\):
\(x_2 - x_1=-7-(-3)=-7 + 3=-4\)
\(y_2 - y_1=1 - 7=-6\)

Then, find the squares of these differences:
\((x_2 - x_1)^2=(-4)^2 = 16\)
\((y_2 - y_1)^2=(-6)^2=36\)

Next, add these squares:
\(16 + 36=52\)

Finally, take the square root:
\(d=\sqrt{52}\approx7.2\) (rounded to the nearest tenth)

Answer:

\(7.2\)