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Chapter 1: Problem 22

Find the distance between the points. $$(9.5,-2.6),(-3.9,8.2)$$

Short Answer

Expert verified
The distance between the given points is approximately 17.21 units.

Step by step solution

01

Understand the Problem and the Formula

We are given two points in the form: (x1, y1) and (x2, y2). The formula to calculate the distance 'd' between these two points, defined by the Euclidean distance, is: \[d = \sqrt{(x2-x1)^2 + (y2-y1)^2}\] Where x1, y1 are the coordinates of the first point and x2, y2 are the coordinates of the second point.
02

Substitute Values into the Formula

Now take the coordinates given and substitute them into the formula. In this case (x1, y1) corresponds to (9.5, -2.6) and (x2, y2) corresponds to (-3.9, 8.2). Therefore we get the new equation: \[d = \sqrt{(-3.9-9.5)^2 + (8.2-(-2.6))^2}\]
03

Perform the Calculations

Next, we calculate the values inside the parentheses, square them, add them together, and then find the square root of the result to get the final answer.\[d = \sqrt{(-13.4)^2 + (10.8)^2} = \sqrt{179.56 + 116.64} = \sqrt{296.2}\]
04

Simplify and Give Final Answer

Finally, we calculate the square root of 296.2 using a calculator and round off the answer to two decimal places. The distance 'd' between the given points is approximately 17.21 units.

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