Answer :
To find the midpoint of the line segment with endpoints [tex]\((-3, 2)\)[/tex] and [tex]\((1, -2)\)[/tex], we will use the midpoint formula. This formula states that 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]
Now, let's substitute the coordinates of the given endpoints into the formula:
- The coordinates of the first endpoint are [tex]\( (x_1, y_1) = (-3, 2) \)[/tex]
- The coordinates of the second endpoint are [tex]\( (x_2, y_2) = (1, -2) \)[/tex]
Plugging these values into the midpoint formula gives:
[tex]\[ M = \left( \frac{-3 + 1}{2}, \frac{2 - 2}{2} \right) \][/tex]
Simplifying each part separately, we get:
- For the x-coordinate of the midpoint:
[tex]\[ \frac{-3 + 1}{2} = \frac{-2}{2} = -1 \][/tex]
- For the y-coordinate of the midpoint:
[tex]\[ \frac{2 - 2}{2} = \frac{0}{2} = 0 \][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ M = (-1, 0) \][/tex]
So, the midpoint of the line segment with endpoints [tex]\((-3, 2)\)[/tex] and [tex]\((1, -2)\)[/tex] is [tex]\((-1, 0)\)[/tex].
[tex]\[ M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \][/tex]
Now, let's substitute the coordinates of the given endpoints into the formula:
- The coordinates of the first endpoint are [tex]\( (x_1, y_1) = (-3, 2) \)[/tex]
- The coordinates of the second endpoint are [tex]\( (x_2, y_2) = (1, -2) \)[/tex]
Plugging these values into the midpoint formula gives:
[tex]\[ M = \left( \frac{-3 + 1}{2}, \frac{2 - 2}{2} \right) \][/tex]
Simplifying each part separately, we get:
- For the x-coordinate of the midpoint:
[tex]\[ \frac{-3 + 1}{2} = \frac{-2}{2} = -1 \][/tex]
- For the y-coordinate of the midpoint:
[tex]\[ \frac{2 - 2}{2} = \frac{0}{2} = 0 \][/tex]
Therefore, the coordinates of the midpoint are:
[tex]\[ M = (-1, 0) \][/tex]
So, the midpoint of the line segment with endpoints [tex]\((-3, 2)\)[/tex] and [tex]\((1, -2)\)[/tex] is [tex]\((-1, 0)\)[/tex].
