Does adding 7+2 and then dividing by 2 help you find the midpoint of the line segment JK?

Question

( the coordinates for the line segment for JK are (-6,7) and (4,2))
A. No, because 7 should be added to 3, then multiplied by 3 to find the midpoint
B. No because (7,2) is not the coordinate of points for J or K.
C. Yes because (7+2)/2 calculates the average, or midpoint of the x-coordinates of points J and K
D.Yes because (7+2)/2 calculates the average, or midpoint of the y-coordinates of points J and K

Answer 1

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

For the line segment JK with the coordinates J(-6, 7) and K(4, 2):

1. X-coordinates: -6 and 4

   • Midpoint x-coordinate: \((-6 + 4) / 2 = -2 / 2 = -1\)

2. Y-coordinates: 7 and 2

   • Midpoint y-coordinate: \((7 + 2) / 2 = 9 / 2 = 4.5\)

The midpoint is then \((-1, 4.5)\).

Now, looking at your options:

• Option A is incorrect because it does not correctly address how to find the midpoint.
• Option B is incorrect because while it mentions that (7, 2) does not correspond to points J or K, it doesn't provide a relevant answer to the question of finding the midpoint.
• Option C is incorrect because (7 + 2) is actually calculating the average of the y-coordinates, not the x-coordinates.
• Option D is correct because (7 + 2)/2 calculates the average (midpoint) of the y-coordinates of points J and K.

Therefore, the correct answer is:

D. Yes because (7+2)/2 calculates the average, or midpoint of the y-coordinates of points J and K.