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Answer :

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).