Question

Using the coordinates, how would adding 6+2 then dividing by 2 help you find the midpoint of line AB?
Coordinate A(2,-2)
Coordinate B(6,5)
A. It finds the sole midpoint of points A and B
B. It finds the average distance between the two x-values of points A and B
C. It finds the distance between points A and B
D. It finds the average distance between the two y-values of points A and B

Answer 1

To find the midpoint of the line segment connecting points A and B given by the coordinates A(2,-2) and B(6,5), you use the midpoint formula, which is \((\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\).

In this case, the x-coordinates of points A and B are 2 and 6, respectively. So, calculating the midpoint for the x-coordinates:

\[
\frac{2 + 6}{2} = \frac{8}{2} = 4
\]

Next, for the y-coordinates of points A and B, which are -2 and 5:

\[
\frac{-2 + 5}{2} = \frac{3}{2} = 1.5
\]

Thus, the midpoint M of line segment AB is at the coordinates (4, 1.5).

Now, considering the options given:

- **A. It finds the sole midpoint of points A and B**: This is true, but it lacks specificity on how it applies to the calculations in your question.
- **B. It finds the average distance between the two x-values of points A and B**: This is not correct; it finds the average of the x-coordinates, not the distance.
- **C. It finds the distance between points A and B**: This is incorrect; it does not give the distance between the two points.
- **D. It finds the average distance between the two y-values of points A and B**: This is similarly incorrect; it finds the average of the y-coordinates.

The correct choice, if looking for how to arrive at the midpoint, would most closely match option **A**, as that is what the calculations ultimately accomplish. However, it should be emphasized that the values derived from averaging the x-coordinates and y-coordinates result in identifying the midpoint itself, not an average distance.