Question

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

Explanation:

Step1: Identify the 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, $x_1 = 4,y_1=-5,x_2 = 7,y_2=-9$.

Step2: Calculate the differences

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

Step3: Square the differences

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

Step4: Sum the squared differences

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

Step5: Take the square - root

$d=\sqrt{25}=5$.

Answer:

D. 5 units