Question

find the distance between the pair of points. (-2,2) and (3,-2) 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 \((x_2,y_2)=(3,-2)\)

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

Substitute the values: \(d=\sqrt{(3-(-2))^2+(-2 - 2)^2}\)

Step3: Simplify the expression inside the square root

\(3-(-2)=3 + 2=5\) and \(-2-2=-4\)
So \(d=\sqrt{5^2+(-4)^2}=\sqrt{25 + 16}\)

Step4: Calculate the sum

\(25+16 = 41\), so \(d=\sqrt{41}\)

Step5: Approximate \(\sqrt{41}\)

\(\sqrt{41}\approx6.403\) (using a calculator)

Answer:

The exact distance is \(\sqrt{41}\) units. The distance is approximately \(6.403\) units.