Select the correct answer.

The endpoints of [tex]$\overline{GH}$[/tex] are [tex]$G(14,3)$[/tex] and [tex]$H(10,-6)$[/tex]. What is the midpoint of [tex]$\overline{GH}$[/tex]?

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]



Answer :

To find the midpoint of a line segment with endpoints [tex]\( G(14, 3) \)[/tex] and [tex]\( H(10, -6) \)[/tex], we can use the midpoint formula. The midpoint formula is:

[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]

Here, the coordinates of [tex]\( G \)[/tex] are [tex]\( (x_1, y_1) = (14, 3) \)[/tex] and the coordinates of [tex]\( H \)[/tex] are [tex]\( (x_2, y_2) = (10, -6) \)[/tex].

1. Calculate the x-coordinate of the midpoint:
[tex]\[ \frac{x_1 + x_2}{2} = \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]

2. Calculate the y-coordinate of the midpoint:
[tex]\[ \frac{y_1 + y_2}{2} = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5 \][/tex]

Thus, the midpoint of [tex]\(\overline{GH}\)[/tex] is:
[tex]\[ \left( 12, -1.5 \right) \][/tex]

So, the correct answer is:
[tex]\[ \boxed{\left(12, -\frac{3}{2}\right)} \][/tex]

Therefore, the answer is:
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]