Answer:
[tex](-2,-2)[/tex].
Step-by-step explanation:
Let us assume that coordinates of other endpoint are [tex](x_1,y_1)[/tex]
We have been given that the midpoint of a segment is (4,3) and one endpoint is (10,8). We are asked to find the coordinates of the other endpoint.
We will use midpoint formula to solve our given problem.
[tex]x\text{-coordinate of midpoint}=\frac{x_1+x_2}{2}[/tex]
[tex]y\text{-coordinate of midpoint}=\frac{y_1+y_2}{2}[/tex]
Upon using our given information, we will get:
[tex]4=\frac{x_1+10}{2}[/tex]
[tex]4\cdot 2=\frac{x_1+10}{2}\cdot 2[/tex]
[tex]8=x_1+10[/tex]
[tex]8-10=x_1+10-10[/tex]
[tex]x_1=-2[/tex]
Similarly, we will find y-coordinate.
[tex]3=\frac{y_1+8}{2}[/tex]
[tex]3\cdot 2=\frac{y_1+8}{2}\cdot 2[/tex]
[tex]6=y_1+8[/tex]
[tex]6-8=y_1+8-8[/tex]
[tex]y_1=-2[/tex]
Therefore, the coordinates of other endpoint would be [tex](-2,-2)[/tex].
