To find the midpoint of a segment with given endpoints [tex]\((4, 5)\)[/tex] and [tex]\((10, -3)\)[/tex], follow these steps:
1. Identify the coordinates of the endpoints:
- The first endpoint is [tex]\((4, 5)\)[/tex], where [tex]\( x_1 = 4 \)[/tex] and [tex]\( y_1 = 5 \)[/tex].
- The second endpoint is [tex]\((10, -3)\)[/tex], where [tex]\( x_2 = 10 \)[/tex] and [tex]\( y_2 = -3 \)[/tex].
2. Use the midpoint formula:
The midpoint [tex]\((M_x, M_y)\)[/tex] of a segment with endpoints [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] can be calculated using the formulas:
[tex]\[
M_x = \frac{x_1 + x_2}{2}
\][/tex]
[tex]\[
M_y = \frac{y_1 + y_2}{2}
\][/tex]
3. Calculate the [tex]\(x\)[/tex]-coordinate of the midpoint:
[tex]\[
M_x = \frac{4 + 10}{2} = \frac{14}{2} = 7.0
\][/tex]
4. Calculate the [tex]\(y\)[/tex]-coordinate of the midpoint:
[tex]\[
M_y = \frac{5 + (-3)}{2} = \frac{5 - 3}{2} = \frac{2}{2} = 1.0
\][/tex]
5. Combine the coordinates:
Thus, the coordinates of the midpoint are [tex]\((7.0, 1.0)\)[/tex].
So, the midpoint of the segment with endpoints [tex]\((4, 5)\)[/tex] and [tex]\((10, -3)\)[/tex] is [tex]\((7.0, 1.0)\)[/tex].
