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Chapter 4: Problem 2

Find the distance between the points (-4,-7) and (-8,-5).

Short Answer

Expert verified
The distance between the points (-4, -7) and (-8, -5) is \(\sqrt{20}\).

Step by step solution

01

Identify the coordinates of the two points

We are given the coordinates of point A as (-4, -7) and point B as (-8, -5). We can label them as follows: Point A: \(x_1 = -4, y_1 = -7\) Point B: \(x_2 = -8, y_2 = -5\)
02

Calculate the difference in x-coordinates and y-coordinates

Using the coordinates of the points, we will find the difference in the x-coordinates and y-coordinates: Difference in x-coordinates: \((x_2 - x_1) = (-8) - (-4) = -8 + 4 = -4\) Difference in y-coordinates: \((y_2 - y_1) = (-5) - (-7) = -5 + 7 = 2\)
03

Apply the distance formula

Now we will apply the distance formula to find the distance between the two points: \(D = \sqrt{(-4)^2 + (2)^2} = \sqrt{16 + 4}\)
04

Compute the distance

Add 16 and 4 inside the square root: \(D = \sqrt{20}\) The distance between the points (-4, -7) and (-8, -5) is \(\sqrt{20}\).

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