Question

question 10 of 10
if a = (-2, -4) and b = (-8, 4), what is the length of \\(\overline{ab}\\)?

a. 12 units

b. 14 units

c. 10 units

d. 16 units

Explanation:

Step1: Recall distance formula

For two points \((x_1,y_1)\) and \((x_2,y_2)\), distance \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Here, \(x_1=-2,y_1 = - 4,x_2=-8,y_2 = 4\)

Step2: Substitute values into formula

First, calculate \(x_2 - x_1=-8-(-2)=-8 + 2=-6\)
Then, calculate \(y_2 - y_1=4-(-4)=4 + 4 = 8\)

Step3: Compute squares and sum

\((x_2 - x_1)^2=(-6)^2 = 36\)
\((y_2 - y_1)^2=8^2 = 64\)
Sum: \(36+64 = 100\)

Step4: Take square root

\(d=\sqrt{100}=10\)

Answer:

C. 10 units