Question

1. what is the distance between points c (2.5, 3.5) and d (-1.5, -4.5) on a coordinate plane?

a. $sqrt{40}$
b. $sqrt{80}$
c. $sqrt{75}$
d. $sqrt{35}$

Explanation:

Step1: Recall 3D distance formula

The distance between 3D points $(x_1,y_1,z_1)$ and $(x_2,y_2,z_2)$ is:
$$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}$$

Step2: Substitute given coordinates

Let $(x_1,y_1,z_1)=(2.5,3.5,5)$ and $(x_2,y_2,z_2)=(-1.5,-4.5,5)$:
$$d=\sqrt{(-1.5-2.5)^2+(-4.5-3.5)^2+(5-5)^2}$$

Step3: Calculate each term

$$d=\sqrt{(-4)^2+(-8)^2+0^2}=\sqrt{16+64+0}$$

Step4: Simplify the expression

$$d=\sqrt{80}$$

Answer:

b. $\sqrt{80}$