Question

1. you are given the following points on a coordinate plane: x(-3, 3.3), y(-3, -5.2), and z(4.5, -5.2).

a. what is the distance (number of units) between points x and y?
b. what is the distance (number of units) between points y and z?

Explanation:

Step1: Identify distance formula for 2D

For points $(x_1,y_1)$ and $(x_2,y_2)$, distance $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Calculate distance X to Y

Substitute $X(-3,3.3), Y(-3,-5.2)$:
$d_{XY}=\sqrt{(-3-(-3))^2+(-5.2-3.3)^2}=\sqrt{0+(-8.5)^2}=\sqrt{72.25}$

Step3: Simplify X-Y distance

$\sqrt{72.25}=8.5$

Step4: Calculate distance Y to Z

Substitute $Y(-3,-5.2), Z(4.5,-5.2)$:
$d_{YZ}=\sqrt{(4.5-(-3))^2+(-5.2-(-5.2))^2}=\sqrt{(7.5)^2+0}=\sqrt{56.25}$

Step5: Simplify Y-Z distance

$\sqrt{56.25}=7.5$

Answer:

a. 8.5 units
b. 7.5 units