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Sagot :
We know that
• One endpoint is (16,3).
,• The midpoint is (9,6).
The formula for midpoint is
[tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})_{}[/tex]Where M is the midpoint. We replace the given endpoint and the midpoint.
[tex](9,6)=(\frac{16+x}{2},\frac{3+y}{2})[/tex]Now, we rewrite the equation by coordinates in order to find each variable.
[tex]9=\frac{16+x}{2}[/tex]We multiply the equation by 2.
[tex]\begin{gathered} 2\cdot9=2\cdot\frac{16+x}{2} \\ 18=16+x \end{gathered}[/tex]Then, we subtract 16 on each side.
[tex]\begin{gathered} 18-16=16-16+x \\ x=2 \end{gathered}[/tex]The x-coordinate of the other endpoint is 2.
Similarly, let's find y.
[tex]6=\frac{3+y}{2}[/tex]Multiply the equation by 2.
[tex]\begin{gathered} 6\cdot2=\frac{3+y}{2}\cdot2 \\ 12=3+y \end{gathered}[/tex]Then, subtract 3 on each side.
[tex]\begin{gathered} 12-3=3-3+y \\ y=9 \end{gathered}[/tex]The y-coordinate of the other endpoint is 9.
Therefore, the other endpoint si (2, 9).
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