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Chapter 2: Problem 8

Find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimals places. $$(-2,-6) \text { and }(3,-4)$$

Short Answer

Expert verified
The distance between the points (-2, -6) and (3, -4) is approximately 5.39.

Step by step solution

01

Identify the coordinates

Identify the coordinates for points. For the point (-2, -6), -2 is x1 and -6 is y1. For the point (3, -4), 3 is x2 and -4 is y2.
02

Apply the distance formula

Apply the distance formula using the identified coordinates. Substituting the values gives: \[d = \sqrt{{(3 -(-2))^2 + ((-4)-(-6))^2}}\] Simplify the expression inside the square root.
03

Perform the arithmetic operations

After simplifying, the expression becomes: \[d = \sqrt{{(5)^2 + (2)^2}} = \sqrt{{25 + 4}} = \sqrt{29}\]
04

Convert to decimal and round

The distance d in radical form is \(\sqrt{29}\). Now convert this to decimal and round to two decimal places. The decimal form of \(\sqrt{29}\) is approximately 5.39.

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