Question

question 1 of 10
if a=(4, -5) and b=(7, -9), what is the length of $overline{ab}$?
a. 7 units
b. 5 units
c. 6 units
d. 8 units

Explanation:

Step1: Identify distance - formula

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

Step2: Assign values

Here, $x_1 = 4,y_1=- 5,x_2 = 7,y_2=-9$. Then $x_2 - x_1=7 - 4 = 3$ and $y_2 - y_1=-9-( - 5)=-9 + 5=-4$.

Step3: Calculate the square - terms

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

Step4: Sum the square - terms

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

Step5: Take the square - root

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

Answer:

B. 5 units