Welcome to Westonci.ca, the ultimate question and answer platform. Get expert answers to your questions quickly and accurately. Our platform connects you with professionals ready to provide precise answers to all your questions in various areas of expertise. Explore comprehensive solutions to your questions from a wide range of professionals on our user-friendly platform.
Sagot :
To find the midpoint of a line segment [tex]\(\overline{GH}\)[/tex] given the endpoints [tex]\(G(14, 3)\)[/tex] and [tex]\(H(10, -6)\)[/tex], we use the midpoint formula. The midpoint formula states that the coordinates of the midpoint [tex]\(M\)[/tex] of a line segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] are given by:
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula step by step:
1. Identify the coordinates of the endpoints:
- [tex]\(G(14, 3)\)[/tex]: Here, [tex]\(x_1 = 14\)[/tex] and [tex]\(y_1 = 3\)[/tex].
- [tex]\(H(10, -6)\)[/tex]: Here, [tex]\(x_2 = 10\)[/tex] and [tex]\(y_2 = -6\)[/tex].
2. Calculate the x-coordinate of the midpoint:
[tex]\[ \text{midpoint}_x = \frac{x_1 + x_2}{2} = \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[ \text{midpoint}_y = \frac{y_1 + y_2}{2} = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5 \][/tex]
Therefore, the coordinates of the midpoint [tex]\(M\)[/tex] are:
[tex]\[ M = (12, -1.5) \][/tex]
Given the answer choices:
- A. [tex]\((6, -15)\)[/tex]
- B. [tex]\(\left(-2, -\frac{2}{2}\right)\)[/tex]
- C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
- D. [tex]\((24, -3)\)[/tex]
- E. [tex]\((18, 12)\)[/tex]
The correct answer is:
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
This matches the coordinates [tex]\((12, -1.5)\)[/tex] obtained from our calculations.
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Let's apply this formula step by step:
1. Identify the coordinates of the endpoints:
- [tex]\(G(14, 3)\)[/tex]: Here, [tex]\(x_1 = 14\)[/tex] and [tex]\(y_1 = 3\)[/tex].
- [tex]\(H(10, -6)\)[/tex]: Here, [tex]\(x_2 = 10\)[/tex] and [tex]\(y_2 = -6\)[/tex].
2. Calculate the x-coordinate of the midpoint:
[tex]\[ \text{midpoint}_x = \frac{x_1 + x_2}{2} = \frac{14 + 10}{2} = \frac{24}{2} = 12 \][/tex]
3. Calculate the y-coordinate of the midpoint:
[tex]\[ \text{midpoint}_y = \frac{y_1 + y_2}{2} = \frac{3 + (-6)}{2} = \frac{3 - 6}{2} = \frac{-3}{2} = -1.5 \][/tex]
Therefore, the coordinates of the midpoint [tex]\(M\)[/tex] are:
[tex]\[ M = (12, -1.5) \][/tex]
Given the answer choices:
- A. [tex]\((6, -15)\)[/tex]
- B. [tex]\(\left(-2, -\frac{2}{2}\right)\)[/tex]
- C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
- D. [tex]\((24, -3)\)[/tex]
- E. [tex]\((18, 12)\)[/tex]
The correct answer is:
C. [tex]\(\left(12, -\frac{3}{2}\right)\)[/tex]
This matches the coordinates [tex]\((12, -1.5)\)[/tex] obtained from our calculations.
We appreciate your time on our site. Don't hesitate to return whenever you have more questions or need further clarification. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.