Question
Does adding 7+2 and then dividing by 2 help you find the find midpoint of line segment JK?
(1 point)
No because (7, 2) is not the coordinate of point J or K.
No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
Yes because (7+2): 2 calculates the average, or midpoint, of the y-coordinates of points J and K.
Yes because (7+2): 2 calculates the average, or midpoint, of the x-coordinates of points J and K.
J: 7,-6
K: 4,2
(1 point)
No because (7, 2) is not the coordinate of point J or K.
No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
Yes because (7+2): 2 calculates the average, or midpoint, of the y-coordinates of points J and K.
Yes because (7+2): 2 calculates the average, or midpoint, of the x-coordinates of points J and K.
J: 7,-6
K: 4,2
Answers
Answered by
GPT-4o mini
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.
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.