Question

if a = (0, 0) and b = (6, 3), what is the length of (overline{ab})?

a. 6.71 units

b. 5.20 units

c. 6.24 units

d. 7.73 units

Explanation:

Step1: Recall 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: Identify the coordinates

Here, \(x_1 = 0,y_1 = 0,x_2 = 6,y_2 = 3\).

Step3: Substitute into the formula

Substitute the values into the formula: \(d=\sqrt{(6 - 0)^2+(3 - 0)^2}=\sqrt{6^2 + 3^2}=\sqrt{36 + 9}=\sqrt{45}\).

Step4: Calculate the square root

\(\sqrt{45}\approx6.71\) (rounded to two decimal places).

Answer:

A. 6.71 units