Answer :
To find the midpoint of the line segment with endpoints \( G(14, 3) \) and \( H(10, -6) \), you will apply the midpoint formula. The midpoint formula states:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
where \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.
1. Identify the coordinates of points \( G \) and \( H \):
- \( G(14, 3) \): Here, \( x_1 = 14 \) and \( y_1 = 3 \).
- \( H(10, -6) \): Here, \( x_2 = 10 \) and \( y_2 = -6 \).
2. Plug these values into the midpoint formula:
[tex]\[ \left( \frac{14 + 10}{2}, \frac{3 + (-6)}{2} \right) \][/tex]
3. Calculate the components of the midpoint:
[tex]\[ \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
[tex]\[ \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5 \][/tex]
4. Thus, the coordinates of the midpoint are:
[tex]\[ \left( 12, -1.5 \right) \][/tex]
Therefore, 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 \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the endpoints.
1. Identify the coordinates of points \( G \) and \( H \):
- \( G(14, 3) \): Here, \( x_1 = 14 \) and \( y_1 = 3 \).
- \( H(10, -6) \): Here, \( x_2 = 10 \) and \( y_2 = -6 \).
2. Plug these values into the midpoint formula:
[tex]\[ \left( \frac{14 + 10}{2}, \frac{3 + (-6)}{2} \right) \][/tex]
3. Calculate the components of the midpoint:
[tex]\[ \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
[tex]\[ \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5 \][/tex]
4. Thus, the coordinates of the midpoint are:
[tex]\[ \left( 12, -1.5 \right) \][/tex]
Therefore, the correct answer is:
C. [tex]\(\left( 12, -\frac{3}{2} \right)\)[/tex]
