Question

what is the length of a line segment whose endpoints have coordinates (5,3) and (1,6)? 1. 5 2. 25 3. \\( \sqrt{17} \\) 4. \\( \sqrt{29} \\)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(5,3)\) and \((x_2,y_2)=(1,6)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(1 - 5)^2+(6 - 3)^2}\)

Step3: Calculate the differences

\(1-5=-4\) and \(6 - 3=3\)
So \(d=\sqrt{(-4)^2+3^2}\)

Step4: Calculate the squares

\((-4)^2 = 16\) and \(3^2=9\)
Then \(d=\sqrt{16 + 9}\)

Step5: Sum and take square - root

\(16+9 = 25\), so \(d=\sqrt{25}=5\)

Answer:

1. \(5\)