Question

question 5 of 10
if a = (7, 9) and b = (3, 12), what is the length of \\(\overline{ab}\\)?
a. 7 units
b. 6 units
c. 4 units
d. 5 units

Explanation:

Step1: Recall distance formula

The distance 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 coordinates

Here, \(x_1 = 7\), \(y_1 = 9\), \(x_2 = 3\), \(y_2 = 12\).

Step3: Substitute into formula

Calculate \(x_2 - x_1 = 3 - 7 = -4\) and \(y_2 - y_1 = 12 - 9 = 3\).
Then, \(d = \sqrt{(-4)^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25}\).

Step4: Simplify

\(\sqrt{25} = 5\).

Answer:

D. 5 units