Question

question 10 of 10
if a = (7, 9) and b = (3, 12), what is the length of $overline{ab}$?
a. 4 units
b. 6 units
c. 7 units
d. 5 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, $A=(7,9)$ so $x_1 = 7,y_1 = 9$ and $B=(3,12)$ so $x_2 = 3,y_2 = 12$.

Step2: Calculate differences

$x_2 - x_1=3 - 7=-4$ and $y_2 - y_1=12 - 9 = 3$.

Step3: Square differences

$(x_2 - x_1)^2=(-4)^2 = 16$ and $(y_2 - y_1)^2=3^2 = 9$.

Step4: Sum squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=16 + 9=25$.

Step5: Take square - root

$d=\sqrt{25}=5$. So the length of $\overline{AB}$ is 5 units.

Answer:

D. 5 units