To find the midpoint of a line segment defined by two coordinates, you need to take the average of the x-coordinates and the average of the y-coordinates separately.
Given:
- Coordinate J(-6, 7)
- Coordinate K(4, 2)
Midpoint Calculation
-
X-coordinates:
- \( x_J = -6 \)
- \( x_K = 4 \)
- Midpoint_x = \( \frac{x_J + x_K}{2} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \)
-
Y-coordinates:
- \( y_J = 7 \)
- \( y_K = 2 \)
- Midpoint_y = \( \frac{y_J + y_K}{2} = \frac{7 + 2}{2} = \frac{9}{2} = 4.5 \)
So, the midpoint of line segment JK is \((-1, 4.5)\).
Answer Choices:
A. No because 7 should be added to 3, then multiplied by 2 to find the midpoint.
(Incorrect, this statement is not relevant to the calculations)
B. Yes because (7+2) divided by 2 calculates the average, or midpoint, of the y-coordinates of points J and K.
(Correct)
C. Yes because (7+2) divided by 2 calculates the average, or midpoint, of the x-coordinates of points J and K.
(Incorrect, this refers to y-coordinates, not x-coordinates)
D. No because (7,2) is not the coordinate of point J or K.
(Incorrect, the statement is misleading, while the coordinates are not correct, it does not address the midpoint calculation)
The correct answer is B.