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]
[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]
