Answer :
To find the midpoint of a line segment with given endpoints, you can use the midpoint formula. The midpoint [tex]\((M)\)[/tex] of a line 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]
Given the endpoints [tex]\((-2, -2)\)[/tex] and [tex]\( (4, 6) \)[/tex]:
1. Identify the coordinates of the endpoints:
- The first endpoint [tex]\((x_1, y_1) = (-2, -2)\)[/tex]
- The second endpoint [tex]\((x_2, y_2) = (4, 6)\)[/tex]
2. Apply the midpoint formula:
- Calculate the x-coordinate of the midpoint: [tex]\(\frac{-2 + 4}{2}\)[/tex]
- Calculate the y-coordinate of the midpoint: [tex]\(\frac{-2 + 6}{2}\)[/tex]
3. Compute the x-coordinate:
- [tex]\[ \frac{-2 + 4}{2} = \frac{2}{2} = 1 \][/tex]
4. Compute the y-coordinate:
- [tex]\[ \frac{-2 + 6}{2} = \frac{4}{2} = 2 \][/tex]
Therefore, the midpoint of the line segment with endpoints [tex]\((-2, -2)\)[/tex] and [tex]\( (4, 6)\)[/tex] is [tex]\((1, 2)\)[/tex].
So, the correct answer is:
D. [tex]\((1, 2)\)[/tex]
[tex]\[ M \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints [tex]\((-2, -2)\)[/tex] and [tex]\( (4, 6) \)[/tex]:
1. Identify the coordinates of the endpoints:
- The first endpoint [tex]\((x_1, y_1) = (-2, -2)\)[/tex]
- The second endpoint [tex]\((x_2, y_2) = (4, 6)\)[/tex]
2. Apply the midpoint formula:
- Calculate the x-coordinate of the midpoint: [tex]\(\frac{-2 + 4}{2}\)[/tex]
- Calculate the y-coordinate of the midpoint: [tex]\(\frac{-2 + 6}{2}\)[/tex]
3. Compute the x-coordinate:
- [tex]\[ \frac{-2 + 4}{2} = \frac{2}{2} = 1 \][/tex]
4. Compute the y-coordinate:
- [tex]\[ \frac{-2 + 6}{2} = \frac{4}{2} = 2 \][/tex]
Therefore, the midpoint of the line segment with endpoints [tex]\((-2, -2)\)[/tex] and [tex]\( (4, 6)\)[/tex] is [tex]\((1, 2)\)[/tex].
So, the correct answer is:
D. [tex]\((1, 2)\)[/tex]
