Question

1. what is the formula to calculate the distance between two points on a coordinate plane?

a. (d=(x_2 - x_1)+(y_2 - y_1))
b. (d = sqrt{(x_2 + x_1)^2+(y_2 + y_1)^2})
c. (d=sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2})
d. (d=(x_2 + x_1)-(y_2 + y_1))

Explanation:

Step1: Recall distance - formula concept

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a coordinate - plane is based on the Pythagorean theorem.

Step2: Analyze each option

Option A: $d=(x_2 - x_1)+(y_2 - y_1)$ is incorrect as it does not account for the square - root and the squared terms. Option B: $d = \sqrt{(x_2 + x_1)^2+(y_2 + y_1)^2}$ has incorrect signs in the terms inside the square - root. Option D: $d=(x_2 + x_1)-(y_2 + y_1)$ is also incorrect as it has no square - root and wrong operations. The correct formula is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, which is Option C.

Answer:

C. $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$