Select the correct answer.

The endpoints of [tex]\(\overline{GH}\)[/tex] are [tex]\(Q(-7, 3)\)[/tex] and [tex]\(H(1, -2)\)[/tex]. What is the midpoint of [tex]\(\overline{GH}\)[/tex]?

A. [tex]\(\left(-3, \frac{1}{2}\right)\)[/tex]

B. [tex]\(\left(4, \frac{5}{2}\right)\)[/tex]

C. [tex]\((9, -7)\)[/tex]

D. [tex]\((-6, -1)\)[/tex]



Answer :

To determine the midpoint of a line segment given the endpoints [tex]\( Q(-7, 3) \)[/tex] and [tex]\( H(1, -2) \)[/tex], you can use the midpoint formula. The formula for the midpoint [tex]\( M \)[/tex] of a segment with endpoints [tex]\( (x_1, y_1) \)[/tex] and [tex]\( (x_2, y_2) \)[/tex] is given by:

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

Plugging in the coordinates of [tex]\( Q \)[/tex] and [tex]\( H \)[/tex]:

[tex]\[ M = \left( \frac{-7 + 1}{2}, \frac{3 - 2}{2} \right) \][/tex]

First, compute the x-coordinate of the midpoint:

[tex]\[ \frac{-7 + 1}{2} = \frac{-6}{2} = -3 \][/tex]

Next, compute the y-coordinate of the midpoint:

[tex]\[ \frac{3 - 2}{2} = \frac{1}{2} \][/tex]

Hence, the coordinates of the midpoint [tex]\( M \)[/tex] are:

[tex]\[ M = \left( -3, \frac{1}{2} \right) \][/tex]

Therefore, the correct answer is:

A. [tex]\( \left( -3, \frac{1}{2} \right) \)[/tex]