Question

1. find the distance between the two points in simplest form. (9, -8) and (3,0)

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

Let $(x_1,y_1)=(9, - 8)$ and $(x_2,y_2)=(3,0)$. Then $x_2 - x_1=3 - 9=-6$ and $y_2 - y_1=0-( - 8)=8$.

Step3: Calculate squares

$(x_2 - x_1)^2=(-6)^2 = 36$ and $(y_2 - y_1)^2=8^2 = 64$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=36 + 64=100$.

Step5: Take square - root

$d=\sqrt{100}=10$.

Answer:

$10$