Question

find the distance between the points (8, - 9) and (5, - 3).
a 45
b 9
c 2\sqrt{13}
d 3\sqrt{5}

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: Substitute the values

Let $(x_1,y_1)=(8, - 9)$ and $(x_2,y_2)=(5,-3)$. Then $x_2 - x_1=5 - 8=-3$ and $y_2 - y_1=-3-(-9)=6$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=(-3)^2 = 9$ and $(y_2 - y_1)^2=6^2 = 36$. The sum is $9 + 36=45$.

Step4: Find the square - root

$d=\sqrt{45}=\sqrt{9\times5}=3\sqrt{5}$.

Answer:

D. $3\sqrt{5}$