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Chapter 0: Problem 14

Find the distance between the given pairs of points. $$ (1,0) \text { and }(6,1) $$

Short Answer

Expert verified
The distance between the points (1, 0) and (6, 1) is \(\sqrt{26}\) units.

Step by step solution

01

Identify the coordinates of the given points

We are given the points (1, 0) and (6, 1). Thus, we have: - Point A: \(x_1 = 1\) and \(y_1 = 0\) - Point B: \(x_2 = 6\) and \(y_2 = 1\)
02

Apply the distance formula

Using the distance formula, we calculate the distance between the points A and B: Distance = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
03

Substitute the coordinates into the formula

Now we substitute the coordinates of points A and B into the distance formula: Distance = \(\sqrt{(6 - 1)^2 + (1 - 0)^2}\)
04

Calculate the distance

We simplify the expression inside the square root: Distance = \(\sqrt{(5)^2 + (1)^2}\) Now calculate the squares: Distance = \(\sqrt{25 + 1}\) Finally, add the numbers inside the square root and find its value: Distance = \(\sqrt{26}\) Thus, the distance between the points (1, 0) and (6, 1) is \(\sqrt{26}\) units.

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