To find the midpoint [tex]\( M \)[/tex] of the line segment connecting the points [tex]\( Q(-2, -4) \)[/tex] and [tex]\( R(6, 10) \)[/tex], we use the midpoint formula:
[tex]\[
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
\][/tex]
Where [tex]\((x_1, y_1)\)[/tex] are the coordinates of point [tex]\( Q \)[/tex], and [tex]\((x_2, y_2)\)[/tex] are the coordinates of point [tex]\( R \)[/tex].
1. Coordinates of point [tex]\( Q \)[/tex] are: [tex]\((-2, -4)\)[/tex]
- [tex]\( x_1 = -2 \)[/tex]
- [tex]\( y_1 = -4 \)[/tex]
2. Coordinates of point [tex]\( R \)[/tex] are: [tex]\((6, 10)\)[/tex]
- [tex]\( x_2 = 6 \)[/tex]
- [tex]\( y_2 = 10 \)[/tex]
3. Calculate the [tex]\( x \)[/tex]-coordinate of the midpoint:
[tex]\[
M_x = \frac{x_1 + x_2}{2} = \frac{-2 + 6}{2} = \frac{4}{2} = 2.0
\][/tex]
4. Calculate the [tex]\( y \)[/tex]-coordinate of the midpoint:
[tex]\[
M_y = \frac{y_1 + y_2}{2} = \frac{-4 + 10}{2} = \frac{6}{2} = 3.0
\][/tex]
5. Combine the [tex]\( x \)[/tex]- and [tex]\( y \)[/tex]-coordinates to get the midpoint:
[tex]\[
M = (M_x, M_y) = (2.0, 3.0)
\][/tex]
Therefore, the midpoint [tex]\( M \)[/tex] of the segment connecting points [tex]\( Q \)[/tex] and [tex]\( R \)[/tex] is [tex]\((2.0, 3.0)\)[/tex].
Given the options:
- [tex]\((2, 3)\)[/tex]
- [tex]\((1, -2)\)[/tex]
- [tex]\((-3, 8)\)[/tex]
- [tex]\((-4, -7)\)[/tex]
The correct choice is:
[tex]\((2, 3)\)[/tex].
