Find the midpoint of the segment with the following endpoints. $$ (8,10) \text { and }(4,6) $$

Question

UpStudy AI · Accepted Answer

To find the midpoint of a line segment with endpoints $$(x_1, y_1)$$ and $$(x_2, y_2)$$, we can use the midpoint formula:

$$
M = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)
$$

Given the endpoints $$(8, 10)$$ and $$(4, 6)$$, we can identify:

- $$x_1 = 8$$
- $$y_1 = 10$$
- $$x_2 = 4$$
- $$y_2 = 6$$

Now, we can substitute these values into the midpoint formula:

1. Calculate the x-coordinate of the midpoint:
   $$
   M_x = \frac{8 + 4}{2} = \frac{12}{2} = 6
   $$

2. Calculate the y-coordinate of the midpoint:
   $$
   M_y = \frac{10 + 6}{2} = \frac{16}{2} = 8
   $$

Thus, the midpoint $$M$$ is:

$$
M = (6, 8)
$$

Therefore, the midpoint of the segment with endpoints $$(8, 10)$$ and $$(4, 6)$$ is $$(6, 8)$$.
The midpoint is (6, 8).

Find the midpoint of the segment with the following endpoints. \[ (8,10) \text { and }(4,6) \]