Question

question 10 of 10 if a = (9, 18) and b = (1, 12), what is the length of (overline{ab})? a. 9 units b. 11 units c. 10 units d. 12 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, \(x_1 = 9,y_1 = 18,x_2 = 1,y_2 = 12\).

Step3: Substitute into formula

Calculate \((x_2 - x_1)=1 - 9=-8\) and \((y_2 - y_1)=12 - 18=-6\).
Then \((x_2 - x_1)^2=(-8)^2 = 64\) and \((y_2 - y_1)^2=(-6)^2 = 36\).
Sum: \(64 + 36=100\).
Take square root: \(\sqrt{100}=10\).

Answer:

C. 10 units