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Sagot :
We are given that the end-point of a line segment is (3, 2) and the middle point is (6, -2).
The formula for the middle point of a line segment is given by:
[tex](h,k)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]Where "h" and "k" are the middle points of the segment.
Now, we can set each of the coordinates equal. For the x-coordinates we have:
[tex]h=\frac{x_1+x_2}{2}[/tex]Where:
[tex]x_1,x_2=\text{ coordinates of the end-points}[/tex]Now, we solve for the second end-point.
First, we multiply both sides by 2:
[tex]2h=x_1+x_2[/tex]Now, we subtract x1 from both sides:
[tex]2h-x_1=x_2[/tex]Now, we substitute both sides:
[tex]\begin{gathered} 2(6)-3=x_2 \\ 12-3=x_2 \\ 9=x_2 \end{gathered}[/tex]Now, we solve for the y-coordinate:
[tex]k=\frac{y_2+y_1}{2}[/tex]Now, we multiply both sides by 2 and subtract the first coordinate to both sides:
[tex]2k-y_1=y_2[/tex]Now, we plug in the values:
[tex]\begin{gathered} 2(-2)-2=y_2 \\ -4-2=y_2 \\ -6=y_2 \end{gathered}[/tex]Therefore, the coordinates of the other end-point is:
[tex](x_2,y_2)=(9,-6)[/tex]
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