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Chapter 2: Problem 13

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(0,-\sqrt{3}) \text { and }(\sqrt{5}, 0)$$

Short Answer

Expert verified
The required distance between the points (0, -鈭�3) and (鈭�5, 0) is approximately 2.83.

Step by step solution

01

Identify the coordinates

First, identify the coordinates of the two points. Point A (as the first point) has coordinates, \(x_1=0, y_1 = -\sqrt{3}\) and point B (as the second point) has coordinates, \(x_2 = \sqrt{5}, y_2 = 0\).
02

Apply the Distance formula

Apply the formula for calculating the distance between two points, \(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\). Substituting the given values, we get, \(d = \sqrt{(\sqrt{5}-0)^2 + (0-(-\sqrt{3}))^2}\).
03

Simplify the Expression

Simplify the expression under the square root and obtain the distance in the radical form. The simplified expression will be \(d = \sqrt{5 + 3} = \sqrt{8}\). The distance \(d\) in radical form is \(\sqrt{8}\).
04

Round to two decimal places

Round the value of distance to two decimal places. Since \(\sqrt{8}\) is approximately 2.82842712474, rounding to two decimal places, will give the distance \(d \approx 2.83\).

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