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]\((1, -6)\)[/tex] and [tex]\((-3, 4)\)[/tex], let's substitute these coordinates into the formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ x_{\text{mid}} = \frac{1 + (-3)}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ y_{\text{mid}} = \frac{-6 + 4}{2} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \][/tex]
Therefore, the coordinates of the midpoint are [tex]\((-1, -1)\)[/tex].
So, the correct option is:
A. [tex]\((-1, -1)\)[/tex]
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Given the endpoints [tex]\((1, -6)\)[/tex] and [tex]\((-3, 4)\)[/tex], let's substitute these coordinates into the formula:
1. Calculate the x-coordinate of the midpoint:
[tex]\[ x_{\text{mid}} = \frac{1 + (-3)}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1 \][/tex]
2. Calculate the y-coordinate of the midpoint:
[tex]\[ y_{\text{mid}} = \frac{-6 + 4}{2} = \frac{-6 + 4}{2} = \frac{-2}{2} = -1 \][/tex]
Therefore, the coordinates of the midpoint are [tex]\((-1, -1)\)[/tex].
So, the correct option is:
A. [tex]\((-1, -1)\)[/tex]
