To find the midpoint [tex]\( M \)[/tex] of a segment with given endpoints [tex]\( J(-8, 1) \)[/tex] and [tex]\( K(1, -2) \)[/tex], we use the midpoint formula.
The midpoint formula states:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Here, [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the given endpoints.
For points [tex]\( J(-8, 1) \)[/tex] and [tex]\( K(1, -2) \)[/tex]:
- [tex]\( x_1 = -8 \)[/tex]
- [tex]\( x_2 = 1 \)[/tex]
- [tex]\( y_1 = 1 \)[/tex]
- [tex]\( y_2 = -2 \)[/tex]
Step-by-step, we will now plug these values into the midpoint formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{-8 + 1}{2} = \frac{-7}{2} = -3.5 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{1 + (-2)}{2} = \frac{1 - 2}{2} = \frac{-1}{2} = -0.5 \][/tex]
Therefore, the coordinates of the midpoint [tex]\( M \)[/tex] are:
[tex]\[ M = (-3.5, -0.5) \][/tex]
So, the correct coordinates for the midpoint are [tex]\( (-3.5, -0.5) \)[/tex].
