Question

find the distance between the pair of points. (-2,2) and (2,-5) the exact distance is □ units. (type an exact answer, using radicals as needed.) the distance is approximately □ units. (round to the nearest thousandth as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-2,2)\) and \((x_2,y_2)=(2,-5)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(2-(-2))^2+(-5 - 2)^2}\)

Step3: Simplify the expression inside the square - root

First, \(2-(-2)=2 + 2=4\) and \(-5-2=-7\)
Then \(d=\sqrt{4^2+(-7)^2}=\sqrt{16 + 49}\)

Step4: Calculate the sum inside the square - root

\(16+49 = 65\), so \(d=\sqrt{65}\)

Step5: Approximate the value of \(\sqrt{65}\)

Using a calculator, \(\sqrt{65}\approx8.062\)

Answer:

The exact distance is \(\sqrt{65}\) units.
The distance is approximately \(8.062\) units.