Question

find the length of the segment connecting (1,8) and (5,7). provide an answer accurate to the nearest tenth.

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(1,8)\) and \((x_2,y_2)=(5,7)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(5 - 1)^2+(7 - 8)^2}\)

Step3: Simplify the expression inside the square root

\((5 - 1)^2=16\) and \((7 - 8)^2 = 1\)
So \(d=\sqrt{16 + 1}=\sqrt{17}\)

Step4: Calculate the approximate value

\(\sqrt{17}\approx4.1\)

Answer:

\(4.1\)