Question

Does adding 7 + 2 and then dividing by 2 help you find the find midpoint of line segment JK?
Point J: (-6, 7)
Point K: (4, 2)

A. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates of points J and K.
B. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the x-coordinates of points J and K.
C. No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
D. No because (7, 2) is not the coordinate of point J or K.

Answer 1

To find the midpoint of a line segment defined by two points, you take the average of the x-coordinates and the average of the y-coordinates of those points.

For points J (-6, 7) and K (4, 2):

1. The x-coordinates are -6 and 4.
2. The y-coordinates are 7 and 2.

To calculate the midpoint:

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

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

Putting it all together, the midpoint M is at (-1, 4.5).

Now, examining the options:

A. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates of points J and K. (**This is correct for the y-coordinates.**)

B. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the x-coordinates of points J and K. (**This is incorrect; it refers to y-coordinates, not x-coordinates.**)

C. No because 7 should be added to 3, then multiplied by 2 to find the midpoint. (**This is incorrect; it's not the correct method for finding the midpoint.**)

D. No because (7, 2) is not the coordinate of point J or K. (**This is incorrect, but it is irrelevant to the method of finding the midpoint.**)

The best answer is:
**A. Yes because (7 + 2) divided by 2 calculates the average, or midpoint, of the y-coordinates of points J and K.**