Question

1. estimate the length of each line segment from its graph. then, calculate the exact length. a) a(2,1) b(3,5)

Explanation:

Step1: Identify the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Determine the coordinates

Here, $A(2,1)$ so $x_1 = 2,y_1=1$ and $B(3,5)$ so $x_2 = 3,y_2 = 5$.

Step3: Substitute into the formula

$d=\sqrt{(3 - 2)^2+(5 - 1)^2}=\sqrt{1^2+4^2}=\sqrt{1 + 16}=\sqrt{17}\approx 4.123$.

Answer:

The exact length of the line - segment $AB$ is $\sqrt{17}\approx4.123$.