Question

if a = (0, 0) and b = (2, 5), what is the approximate length of $overline{ab}$?
a. 2.65 units
b. 5.74 units
c. 5.39 units
d. 4.58 units

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 0,y_1 = 0,x_2=2,y_2 = 5$.

Step2: Substitute values

$d=\sqrt{(2 - 0)^2+(5 - 0)^2}=\sqrt{2^2+5^2}=\sqrt{4 + 25}=\sqrt{29}$.

Step3: Calculate approximation

$\sqrt{29}\approx5.39$.

Answer:

C. 5.39 units