Answer :
To find the midpoint of the line segment [tex]\(\overline{GH}\)[/tex] with endpoints [tex]\(G(14,3)\)[/tex] and [tex]\(H(10,-6)\)[/tex], we use the midpoint formula. The midpoint formula for a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is given by:
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the coordinates [tex]\(G(14, 3)\)[/tex] and [tex]\(H(10, -6)\)[/tex], we can substitute these values into the formula. Let's calculate each component step by step.
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \text{x-coordinate} = \frac{14 + 10}{2} \][/tex]
Add the x-coordinates:
[tex]\[ 14 + 10 = 24 \][/tex]
Then divide by 2:
[tex]\[ \frac{24}{2} = 12 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \text{y-coordinate} = \frac{3 + (-6)}{2} \][/tex]
Add the y-coordinates:
[tex]\[ 3 + (-6) = -3 \][/tex]
Then divide by 2:
[tex]\[ \frac{-3}{2} = -1.5 \][/tex]
So, the coordinates of the midpoint are:
[tex]\[ (12, -1.5) \][/tex]
Given the options provided, the correct answer is:
[tex]\[ \text{C.} \quad \left(12, -\frac{3}{2}\right) \][/tex]
This is equivalent to [tex]\((12, -1.5)\)[/tex].
[tex]\[ \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the coordinates [tex]\(G(14, 3)\)[/tex] and [tex]\(H(10, -6)\)[/tex], we can substitute these values into the formula. Let's calculate each component step by step.
1. Calculate the x-coordinate of the midpoint:
[tex]\[ \text{x-coordinate} = \frac{14 + 10}{2} \][/tex]
Add the x-coordinates:
[tex]\[ 14 + 10 = 24 \][/tex]
Then divide by 2:
[tex]\[ \frac{24}{2} = 12 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ \text{y-coordinate} = \frac{3 + (-6)}{2} \][/tex]
Add the y-coordinates:
[tex]\[ 3 + (-6) = -3 \][/tex]
Then divide by 2:
[tex]\[ \frac{-3}{2} = -1.5 \][/tex]
So, the coordinates of the midpoint are:
[tex]\[ (12, -1.5) \][/tex]
Given the options provided, the correct answer is:
[tex]\[ \text{C.} \quad \left(12, -\frac{3}{2}\right) \][/tex]
This is equivalent to [tex]\((12, -1.5)\)[/tex].
Answer:
C. (12, -3/2)
Step-by-step explanation:
Add the values of the x-coordinates and divide by 2.
Add the values of the y-coordinates and divide by 2.
(14 + 10)/2 = 24/2 = 12
(3 + (-6))/2 = -3/2
Answer: C. (12, -3/2)
