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Chapter 2: Problem 1

Find the distance between each pair of points. If necessary, round answers to two decimals places. $$(2,3) \text { and }(14,8)$$

Short Answer

Expert verified
The distance between points (2,3) and (14,8) is 13 units.

Step by step solution

01

Identify the Coordinates

Identify the coordinates of the two points. For our case, the first point is (2,3) and the second point is (14,8). Therefore, \(x_1 = 2\), \(y_1 = 3\), \(x_2 = 14\), and \(y_2 = 8\).
02

Substitute into Formula

Substitute the values of \(x_1\), \(y_1\), \(x_2\), and \(y_2\) into the distance formula. This will give:\[d = \sqrt{(14 - 2)^2 +(8 - 3)^2}\]
03

Simplify

Simplify the equation for easier calculation. This gives:\[d = \sqrt{(12)^2 +(5)^2}\]\[d = \sqrt{144 + 25}\]\[d = \sqrt{169}\]
04

Calculate Distance

Calculate the square root of 169 to find the distance. That is:\[d = 13\]

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