How is the midpoint between two points (X1, Y1) and (X2, Y2) calculated?

How is the midpoint between two points (X1, Y1) and (X2, Y2) calculated?

• A. (X1 + X2, Y1 + Y2)
• B. (X1 - X2)/2, (Y1 - Y2)/2
• C. (X1+X2)/2, (Y1+Y2)/2
• D. (X1*X2)/2, (Y1*Y2)/2

Answer: (C)

The midpoint between two points in a coordinate plane is found by averaging the x-coordinates and the y-coordinates of the two points. This is because the midpoint represents the point that is exactly halfway between the two given points. To calculate the x-coordinate of the midpoint, you add the x-coordinates of the two points, \(X1\) and \(X2\), and then divide that sum by 2. This gives the average x-value: \[ \text{Midpoint x-coordinate} = \frac{X1 + X2}{2} \] Similarly, for the y-coordinate, you add the y-coordinates \(Y1\) and \(Y2\) of the two points and divide by 2 to find the average y-value: \[ \text{Midpoint y-coordinate} = \frac{Y1 + Y2}{2} \] Combining these results, the coordinates of the midpoint are expressed as: \[ \left( \frac{X1 + X2}{2}, \frac{Y1 + Y2}{2} \right) \] This formula ensures that the midpoint is equidistant from both original points, making it the correct choice. The other options

The midpoint between two points in a coordinate plane is found by averaging the x-coordinates and the y-coordinates of the two points. This is because the midpoint represents the point that is exactly halfway between the two given points.

To calculate the x-coordinate of the midpoint, you add the x-coordinates of the two points, (X1) and (X2), and then divide that sum by 2. This gives the average x-value:

[

\text{Midpoint x-coordinate} = \frac{X1 + X2}{2}

]

Similarly, for the y-coordinate, you add the y-coordinates (Y1) and (Y2) of the two points and divide by 2 to find the average y-value:

[

\text{Midpoint y-coordinate} = \frac{Y1 + Y2}{2}

]

Combining these results, the coordinates of the midpoint are expressed as:

[

\left( \frac{X1 + X2}{2}, \frac{Y1 + Y2}{2} \right)

]

This formula ensures that the midpoint is equidistant from both original points, making it the correct choice. The other options