Answer :
To find the midpoint of a line segment with endpoints [tex]\((-4, -3)\)[/tex] and [tex]\( (7, -5) \)[/tex], we can use the midpoint formula. The midpoint formula is given by:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the endpoints.
1. Identify the coordinates of the endpoints:
- [tex]\((x_1, y_1) = (-4, -3)\)[/tex]
- [tex]\((x_2, y_2) = (7, -5)\)[/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{-4 + 7}{2} = \frac{3}{2} = 1.5 \][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{-3 + -5}{2} = \frac{-8}{2} = -4 \][/tex]
4. Combine the x and y coordinates to find the midpoint:
[tex]\[ \left( 1.5, -4 \right) \][/tex]
Thus, the midpoint of the line segment with endpoints [tex]\((-4, -3)\)[/tex] and [tex]\( (7, -5) \)[/tex] is [tex]\( \left(1.5, -4\right) \)[/tex].
The correct answer is:
D. [tex]\(\left(1.5, -4\right)\)[/tex]
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] are the coordinates of the endpoints.
1. Identify the coordinates of the endpoints:
- [tex]\((x_1, y_1) = (-4, -3)\)[/tex]
- [tex]\((x_2, y_2) = (7, -5)\)[/tex]
2. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{-4 + 7}{2} = \frac{3}{2} = 1.5 \][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{-3 + -5}{2} = \frac{-8}{2} = -4 \][/tex]
4. Combine the x and y coordinates to find the midpoint:
[tex]\[ \left( 1.5, -4 \right) \][/tex]
Thus, the midpoint of the line segment with endpoints [tex]\((-4, -3)\)[/tex] and [tex]\( (7, -5) \)[/tex] is [tex]\( \left(1.5, -4\right) \)[/tex].
The correct answer is:
D. [tex]\(\left(1.5, -4\right)\)[/tex]
