AFOQT Practice Test

Which formula represents the midpoint between two points in a coordinate system?

1. (x₁+x₂, y₁+y₂)

2. (x₁-x₂)/2, (y₁-y₂)/2

3. (x₁+x₂)/2, (y₁+y₂)/2

4. (x₂-x₁)/2, (y₂-y₁)/2

The correct answer is: (x₁+x₂)/2, (y₁+y₂)/2

The correct choice derives from the mathematical definition of the midpoint of a line segment connecting two points in a Cartesian coordinate system. The midpoint is calculated by averaging the x-coordinates and the y-coordinates of the points. When you represent the two points as (x₁, y₁) and (x₂, y₂), the midpoint formula specifically involves adding the x-coordinates together and dividing by 2, as well as adding the y-coordinates together and dividing by 2. This results in the formula: \[ \text{Midpoint} = \left(\frac{x₁+x₂}{2}, \frac{y₁+y₂}{2}\right) \] This approach effectively finds the central point that is equidistant from both endpoints on the Cartesian plane, making it a fundamental concept in coordinate geometry.