Question

question 8 of 10 if a = (-1, -3) and b = (11, -8), what is the length of (overline{ab})? a. 12 units b. 13 units c. 14 units d. 11 units

Explanation:

Step1: Recall distance formula

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

Step2: Identify coordinates

Here, \(x_1=-1,y_1 = - 3,x_2 = 11,y_2=-8\).

Step3: Substitute into formula

First, calculate \(x_2 - x_1=11-(-1)=12\) and \(y_2 - y_1=-8 - (-3)=-5\).
Then, \((x_2 - x_1)^2=12^2 = 144\) and \((y_2 - y_1)^2=(-5)^2 = 25\).
Sum these: \(144 + 25=169\).
Take the square root: \(\sqrt{169}=13\).

Answer:

B. 13 units