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Chapter 2: Problem 12

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(2.6,1.3) \text { and }(1.6,-5.7)$$

Short Answer

Expert verified
The distance between the points (2.6, 1.3) and (1.6, -5.7) is approximately \(7.07\).

Step by step solution

01

Identifying Points

The two points given are (2.6, 1.3) and (1.6, -5.7). So, coordinate x1 is 2.6, y1 is 1.3, x2 is 1.6 and y2 is -5.7.
02

Apply Distance Formula

The distance between two points in a two-dimensional space can be found using the distance formula, derived from the Pythagorean Theorem. The formula is: \(d = \sqrt{(x2-x1)^{2} + (y2-y1)^{2}}\). So, substituting x1, x2, y1, and y2 into the formula yields: \(d = \sqrt{ (1.6 - 2.6)^2 + (-5.7 - 1.3)^2}\).
03

Simplification

Simplify the expression within the square root: \(d = \sqrt{ (-1.0)^2 + (-7.0)^2} = \sqrt{1.0 + 49.0} = \sqrt{50.0}\).
04

Rounding to Two Decimal Places

Now, let's calculate the decimal representation for \( \sqrt{50.0}\) and round to two decimal places. The result is approximately 7.07.

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