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Chapter 1: Problem 38

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

Short Answer

Expert verified
The distance between the points (9.5,-2.6) and (-3.9,8.2) is approximately 17.21 units.

Step by step solution

01

Identify the Coordinates

The first point is (9.5, -2.6) and the second point is (-3.9, 8.2). This means \(x_1 = 9.5, y_1 = -2.6, x_2 = -3.9, y_2 = 8.2\)
02

Substitute the Coordinates into the Distance Formula

Substitute the values of \(x_1, y_1, x_2, y_2\) into the formula \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) to get \(d = \sqrt{(-3.9 - 9.5)^2 + (8.2 - (-2.6))^2}\)
03

Simplify the Equation

Calculate the values in the parentheses first to get \(d = \sqrt{(-13.4)^2 + (10.8)^2}\). Then square the numbers inside the square root to get \(d = \sqrt{179.56 + 116.64}\)
04

Further Simplify the Equation

Add the numbers inside the square root to get \(d = \sqrt{296.2}\)
05

Find the Square Root

To find the final distance, calculate the square root of 296.2 to get an approximate value of d. The result is approximately 17.21

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