Question

11.1: distance and midpoint formulas; circles
score: 2/24 answered: 1/18
question 2
find the distance between the points (-1, -2) and (5, 2)
distance =
give an exact answer. simplify any radicals.
question help: video message instructor

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(-1,-2)\) and \((x_2,y_2)=(5,2)\)

Step2: Apply the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(5-(-1))^2+(2 - (-2))^2}\)

Step3: Simplify the expression inside the square - root

First, \(5-(-1)=5 + 1=6\) and \(2-(-2)=2 + 2=4\)
Then \(d=\sqrt{6^2+4^2}=\sqrt{36 + 16}\)

Step4: Calculate the sum and the square - root

\(36+16 = 52\), and \(d=\sqrt{4\times13}\)
Since \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 4\), \(b = 13\)), \(d = 2\sqrt{13}\)

Answer:

\(2\sqrt{13}\)