Question

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

Explanation:

Step1: Identify distance - formula

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

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:

B. 17 units