Question

using the points (-6,7) and (4,2), does adding 7+2 and then dividing by 2 help find the midpoint

no because 7 should be added to 3, then multiplied by 2 to find the midpoint
Yes because (7+2) divided by 2 calculated the average, or midpoint, of the y-coordinate
Yes because (7+2) divided by 2 calculates the average, or midpoint, of the x coordinates
No because (7,2) is not the coordinates

Answer 1

To find the midpoint between two points \((-6,7)\) and \((4,2)\), you use the midpoint formula, which is:

\[
\text{Midpoint} = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\]

For the points given:

- \(x_1 = -6\), \(y_1 = 7\)
- \(x_2 = 4\), \(y_2 = 2\)

You calculate the midpoint as follows:

1. For the x-coordinates:
\[
\frac{-6 + 4}{2} = \frac{-2}{2} = -1
\]

2. For the y-coordinates:
\[
\frac{7 + 2}{2} = \frac{9}{2} = 4.5
\]

Thus, the midpoint is \((-1, 4.5)\).

Now, looking at the options you provided:

- **No**, because 7 should be added to 3, then multiplied by 2 to find the midpoint. (This statement is incorrect; it misinterprets how to find the midpoint.)
- **Yes**, because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates. (This statement is correct.)
- **Yes**, because (7 + 2) divided by 2 calculates the average, or midpoint, of the x-coordinates. (This statement is incorrect; it relates to y-coordinates.)
- **No**, because (7,2) is not the coordinates. (This statement is not relevant to finding the midpoint.)

The most appropriate response based on your options is: **Yes, because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates.**