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Chapter 2: Problem 11

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(3.5,8.2) \text { and }(-0.5,6.2)$$

Short Answer

Expert verified
The distance between the two points (3.5, 8.2) and (-0.5, 6.2) is approximately 4.47.

Step by step solution

01

Identify the coordinates of given points

The first point is (3.5, 8.2), so \(x_1 = 3.5\) and \(y_1 = 8.2\). The second point is (-0.5, 6.2), so \(x_2 = -0.5\) and \(y_2 = 6.2\).
02

Apply the distance formula

Substitute the identified coordinates into the distance formula. \[d = \sqrt{(-0.5 - 3.5)^2 + (6.2 - 8.2)^2}\]
03

Simplify and calculate

Simplify and calculate the expression inside the square root. \[d = \sqrt{(-4)^2 + (-2)^2} = \sqrt{16 + 4} = \sqrt{20}\]
04

Express in simplified radical form

The number 20 can be expressed as the product of 4 and 5, where 4 is a perfect square. So, the square root of 20 becomes \(2\sqrt{5}\).
05

Round to two decimal places

Convert the simplified radical form to a decimal and round it to two decimal places. So, \(d \approx 4.47\).

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