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To determine the midpoint of a line segment, we use the midpoint formula. The midpoint [tex]\((M_x, M_y)\)[/tex] of a line segment with endpoints [tex]\(G(x_1, y_1)\)[/tex] and [tex]\(H(x_2, y_2)\)[/tex] is given by:
[tex]\[ M_x = \frac{x_1 + x_2}{2} \][/tex]
[tex]\[ M_y = \frac{y_1 + y_2}{2} \][/tex]
Given the endpoints [tex]\(G(14, 3)\)[/tex] and [tex]\(H(10, -6)\)[/tex], we can substitute the coordinates into the midpoint formula.
First, calculate the x-coordinate of the midpoint:
[tex]\[ M_x = \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
Next, calculate the y-coordinate of the midpoint:
[tex]\[ M_y = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -\frac{3}{2} \][/tex]
So, the midpoint of [tex]\(\overline{GH}\)[/tex] is:
[tex]\[ \left(12, -\frac{3}{2}\right) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\left(12, -\frac{3}{2}\right)} \][/tex]
[tex]\[ M_x = \frac{x_1 + x_2}{2} \][/tex]
[tex]\[ M_y = \frac{y_1 + y_2}{2} \][/tex]
Given the endpoints [tex]\(G(14, 3)\)[/tex] and [tex]\(H(10, -6)\)[/tex], we can substitute the coordinates into the midpoint formula.
First, calculate the x-coordinate of the midpoint:
[tex]\[ M_x = \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
Next, calculate the y-coordinate of the midpoint:
[tex]\[ M_y = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -\frac{3}{2} \][/tex]
So, the midpoint of [tex]\(\overline{GH}\)[/tex] is:
[tex]\[ \left(12, -\frac{3}{2}\right) \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{\left(12, -\frac{3}{2}\right)} \][/tex]
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