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Chapter 1: Problem 18

Find the distance between the points. $$(8,5),(0,20)$$

Short Answer

Expert verified
The distance between the points (8,5) and (0,20) is 17 units.

Step by step solution

01

Identify the coordinates

The two points given are (8,5) and (0,20). So, \(x_1 = 8\), \(y_1 = 5\), \(x_2 = 0\), and \(y_2 = 20\).
02

Substitute the values into the distance formula

Substitute the values into the formula: \[d = \sqrt{(0 - 8)^2 + (20 - 5)^2}\]
03

Simplify the equation

Simplify the equation: \[d = \sqrt{(-8)^2 + 15^2}\]
04

Calculate the squares

Calculate the squared numbers: \[d = \sqrt{64 + 225}\]
05

Add the numbers under the square root

Add these numbers together: \[d = \sqrt{289}\]
06

Take the square root

The square root of 289 is 17, so: \[d = 17\]

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