What is the midpoint formula between two points (x1, y1) and (x2, y2)?

What is the midpoint formula between two points (x1, y1) and (x2, y2)?

• A. M = ((x1 + x2)/2, (y1 + y2)/2)
• B. M = (x1 + x2, y1 + y2)
• C. M = (x1 + x2, (y1 + y2)/2)
• D. M = ((x1 - x2)/2, (y1 - y2)/2)

Answer: (A)

The midpoint formula is used to find the point that is exactly halfway between two given points in a Cartesian coordinate system. This is particularly useful in various applications such as geometry, computer graphics, and even real-life situations like finding the center point between two locations. To derive the formula, consider two points: (x1, y1) and (x2, y2). To find the midpoint, you essentially need to average the x-coordinates and the y-coordinates of these two points. The x-coordinate of the midpoint is calculated as the average of the x-coordinates: \((x1 + x2)/2\). Similarly, the y-coordinate of the midpoint is calculated as the average of the y-coordinates: \((y1 + y2)/2\). Combining these two results gives us the complete midpoint formula: \[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) \] This correctly captures the notion of finding the exact midpoint between the two points. Thus, the answer is correct because it accurately represents the mathematical principle behind calculating a midpoint in a two-dimensional space.

The midpoint formula is used to find the point that is exactly halfway between two given points in a Cartesian coordinate system. This is particularly useful in various applications such as geometry, computer graphics, and even real-life situations like finding the center point between two locations.

To derive the formula, consider two points: (x1, y1) and (x2, y2). To find the midpoint, you essentially need to average the x-coordinates and the y-coordinates of these two points.

The x-coordinate of the midpoint is calculated as the average of the x-coordinates: ((x1 + x2)/2). Similarly, the y-coordinate of the midpoint is calculated as the average of the y-coordinates: ((y1 + y2)/2).

Combining these two results gives us the complete midpoint formula:

[ M = \left( \frac{x1 + x2}{2}, \frac{y1 + y2}{2} \right) ]

This correctly captures the notion of finding the exact midpoint between the two points. Thus, the answer is correct because it accurately represents the mathematical principle behind calculating a midpoint in a two-dimensional space.