The formula for calculating the midpoint of a line segment is given below
[tex](x,y)=\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2}[/tex]Where the values are
[tex]\begin{gathered} x=5,y=-4 \\ x_1=5,y_1=-1 \end{gathered}[/tex]By substituting the values, we will have
[tex]\begin{gathered} (x,y)=\frac{(x_1+x_2)}{2},\frac{(y_1+y_2)}{2} \\ (5,-4)=\frac{(5_{}+x_2)}{2},\frac{(-1_{}+y_2)}{2} \end{gathered}[/tex]By comparing coefficient, we will have
[tex]\begin{gathered} \frac{(5_{}+x_2)}{2}=5 \\ \frac{(-1_{}+y_2)}{2}=-4 \end{gathered}[/tex]Cross multiply to get the values of x2
[tex]\begin{gathered} \frac{(5_{}+x_2)}{2}=5 \\ 5+x_2=10 \\ \text{substract 5 from both sides} \\ 5-5+x_2=10-5 \\ x_2=5 \end{gathered}[/tex]Cross multiply to get the values of y2
[tex]\begin{gathered} \frac{(-1_{}+y_2)}{2}=-4 \\ -1+y_2=-8 \\ \text{add 1 to both sides} \\ -1+1+y_2=-8+1_{} \\ y_2=-7 \end{gathered}[/tex]Hence,
The coordinate of the other endpoint is ( 5, -7 )
