Question

question 3 of 10 if a = (10, 4) and b = (2, 19), what is the length of $overline{ab}$? a. 15 units b. 12 units c. 17 units d. 23 units

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 10,y_1 = 4,x_2 = 2,y_2 = 19$.

Step2: Calculate differences

$x_2 - x_1=2 - 10=-8$ and $y_2 - y_1=19 - 4 = 15$.

Step3: Square the differences

$(x_2 - x_1)^2=(-8)^2 = 64$ and $(y_2 - y_1)^2=15^2 = 225$.

Step4: Sum the squared differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 225=289$.

Step5: Take the square - root

$d=\sqrt{289}=17$.

Answer:

C. 17 units