Answer :
To find the midpoint of a line segment given its endpoints, 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.
Here, we have:
- [tex]\( G(14, 3) \)[/tex]
- [tex]\( H(10, -6) \)[/tex]
Let's apply the midpoint formula step by step:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{G_x + H_x}{2} = \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{G_y + H_y}{2} = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5 \][/tex]
Therefore, the midpoint of [tex]\(\overline{GH}\)[/tex] is [tex]\((12, -1.5)\)[/tex].
Now, we need to find the corresponding answer choice:
A. [tex]\((6, -15)\)[/tex]
B. [tex]\(\left(-2, -\frac{9}{2}\right)\)[/tex]
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
D. [tex]\((24, -3)\)[/tex]
E. [tex]\((18, 12)\)[/tex]
The correct answer is:
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/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.
Here, we have:
- [tex]\( G(14, 3) \)[/tex]
- [tex]\( H(10, -6) \)[/tex]
Let's apply the midpoint formula step by step:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{G_x + H_x}{2} = \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{G_y + H_y}{2} = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5 \][/tex]
Therefore, the midpoint of [tex]\(\overline{GH}\)[/tex] is [tex]\((12, -1.5)\)[/tex].
Now, we need to find the corresponding answer choice:
A. [tex]\((6, -15)\)[/tex]
B. [tex]\(\left(-2, -\frac{9}{2}\right)\)[/tex]
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
D. [tex]\((24, -3)\)[/tex]
E. [tex]\((18, 12)\)[/tex]
The correct answer is:
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
