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Chapter 1: Problem 34

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

Short Answer

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

Step by step solution

01

Identify the Points

The first task is to identify the points provided. The points given in the problem are (1,3) and (3,-2). This means the coordinates for the first point are x1 = 1 and y1 = 3. The coordinates for the second point are x2 = 3 and y2 = -2.
02

Apply the Distance Formula

Using the distance formula, \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\), replace x1, y1, x2, y2 with the actual coordinates of the points. This means we will calculate \(d = \sqrt{(3-1)^2 + (-2-3)^2}\)
03

Simplify the Equation

Now simplify the equation to get the distance. This will result in \(d = \sqrt{(2)^2 + (-5)^2}\) which further simplifies to \(d = \sqrt{4 + 25}\).
04

Calculate the distance

Now our equation becomes \(d = \sqrt{29}\). This is the computed distance between the two points.

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