Question

find the distance between the pair of points. (-3,5) and (2,-2) the exact distance is units. (type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-3,5)\) and \((x_2,y_2)=(2,-2)\)

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

Substitute the values: \(d=\sqrt{(2-(-3))^2+(-2 - 5)^2}\)

Step3: Simplify the expressions inside the square - root

First, \(2-(-3)=2 + 3=5\) and \(-2-5=-7\)
So \(d=\sqrt{5^2+(-7)^2}\)

Step4: Calculate the squares

\(5^2 = 25\) and \((-7)^2=49\)
Then \(d=\sqrt{25 + 49}\)

Step5: Add the numbers inside the square - root

\(25+49 = 74\)
So \(d=\sqrt{74}\)

Answer:

\(\sqrt{74}\)