Question

Does adding 7+2 and then dividing by 2 help you find the find midpoint of line segment JK¯¯¯¯¯¯¯¯ ? (1 point) Responses No because 7 should be added to 3, then multiplied by 2 to find the midpoint. No because 7 should be added to 3, then multiplied by 2 to find the midpoint. No because (7,2) is not the coordinate of point J or K. No because open paren 7 comma 2 close paren is not the coordinate of point J or K. Yes because (7+2)÷2 calculates the average, or midpoint, of the x-coordinates of points J and K. Yes because open paren 7 plus 2 close paren divided by 2 calculates the average, or midpoint, of the x -coordinates of points J and K. Yes because (7+2)÷2 calculates the average, or midpoint, of the y-coordinates of points J and K.

The values of J and K are, J: (-6, 7) and K: (4, 2)

Answer 1

To find the midpoint \( M \) of a line segment defined by two endpoints \( J(x_1, y_1) \) and \( K(x_2, y_2) \), you can use the midpoint formula:

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

Given the coordinates of points \( J(-6, 7) \) and \( K(4, 2) \):

- The x-coordinates are \(-6\) and \(4\).
- The y-coordinates are \(7\) and \(2\).

Calculating the midpoints:

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

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

Thus, the midpoint \( M \) is:
\[
M = \left( -1, 4.5 \right)
\]

Now, regarding the initial question about adding \( 7 + 2 \) and dividing by \( 2 \):

The expression \( (7 + 2) \div 2 \) indeed calculates the average of the y-coordinates of points \( J \) and \( K\), which gives \( 4.5 \) - the y-coordinate of the midpoint.

However, it does not help find the x-coordinate's midpoint since it deals specifically with the y-coordinates.

Among the provided options, the most accurate response is:
- **Yes because (7+2)÷2 calculates the average, or midpoint, of the y-coordinates of points J and K.**

This choice correctly identifies that the operation performed gives you the y-coordinate of the midpoint, though it is important to note that you would need to consider both x and y coordinates to fully determine the midpoint of the line segment.