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Chapter 1: Problem 20

Find the distance between the points. $$(1,3),(3,-2)$$

Short Answer

Expert verified
The distance between points (1,3) and (3,-2) is \(\sqrt{29}\)

Step by step solution

01

Identify the Points

The first point is (1,3) and the second point is (3,-2). So, our \(x_1 = 1\), \(y_1 = 3\), \(x_2 = 3\) and \(y_2 = -2\)
02

Calculate Differences

Find the change in x and y. \(x_2 - x_1 = 3 - 1 = 2\), \(y_2 - y_1 = -2 - 3 = -5\)
03

Apply Pythagorean Theorem

Calculate the distance by finding the square root of the sum of the squares of the differences. The formula from the theorem is \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\). Plugging in the values, we get \(d = \sqrt{(2)^2 + (-5)^2} = \sqrt{(4) + (25)} = \sqrt{29}\)

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