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Chapter 1: Problem 32

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

Short Answer

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

Step by step solution

01

Identify the coordinates of the points

The coordinates given are $(8,5)$ and $(0,20)$. Thus, \(x_1 = 8, y_1 = 5, x_2 = 0, y_2 = 20\).
02

Apply the formula

Insert these values into the formula for two-dimensional Euclidean Distance, which is \(\sqrt{{(x_2 - x_1)}^2 + {(y_2 - y_1)}^2}\). Thus, we get \(\sqrt{{(0 - 8)}^2 + {(20 - 5)}^2}\).
03

Simplify the expression

Simplify the expression inside the square root to get \(\sqrt{{(-8)}^2 + {15}^2} = \sqrt{64 + 225} = \sqrt{289}\).
04

Compute the square root

The square root of 289 is 17.
05

Write out the answer

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

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