To find the midpoint of a line segment given its endpoints, you take the average of the x-coordinates and the average of the y-coordinates of the two points.
The coordinates for points J and K are:
- J: (7, -6)
- K: (4, 2)
Step 1: Average the x-coordinates
\[ \text{Midpoint x-coordinate} = \frac{x_1 + x_2}{2} = \frac{7 + 4}{2} = \frac{11}{2} = 5.5 \]
Step 2: Average the y-coordinates
\[ \text{Midpoint y-coordinate} = \frac{y_1 + y_2}{2} = \frac{-6 + 2}{2} = \frac{-4}{2} = -2 \]
Thus, the midpoint M of the line segment JK is at: \[ M: \left(5.5, -2\right) \]
Evaluate the response options:
- No because (7, 2) is not the coordinate of point J or K. (Incorrect; it’s not relevant to the calculation of the midpoint.)
- No because 7 should be added to 3, then multiplied by 2 to find the midpoint. (Incorrect; this statement is not relevant to the given points.)
- Yes because (7+2): 2 calculates the average, or midpoint, of the y-coordinates of points J and K. (Wrong; the correct average for the y-coordinates is -6 and 2.)
- Yes because (7+2): 2 calculates the average, or midpoint, of the x-coordinates of points J and K. (Incorrect; the average for x-coordinates is calculated with 7 and 4, not 7 and 2.)
Conclusion
None of the options accurately explain the calculation for finding the midpoint. The calculations use the x-coordinates 7 and 4, and the y-coordinates -6 and 2, rather than the values 7 and 2 used in the multiple-choice answers.
1 answer