Given:
The midpoint of a line PQ is M = (1,-5).
THe coordinate of point P = (6,-8).
The objective is to find the coordinate of other point Q.
Explanation:
Since, M is the midpoint of PQ, the distance between PM and QM will be equal.
Consider the coordinate of P , M and Q as,
[tex]\begin{gathered} P(x_1,y_1)=P(6,-8) \\ M(x,y)=(1,-5) \\ Q\mleft(x_2,y_2\mright) \end{gathered}[/tex]The general midpoint formula is,
[tex]\begin{gathered} M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \\ (x,y)=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}) \end{gathered}[/tex]To find the value of x value of point Q:
By equating only the variables of x,
[tex]\begin{gathered} x=\frac{x_1+x_2}{2} \\ 1=\frac{6+x_2}{2} \\ 1(2)=6+x_2_{} \\ x_2=2-6 \\ x_2=-4 \end{gathered}[/tex]To find the value of y value of point Q:
By equating only the variable of y,
[tex]\begin{gathered} y=\frac{y_1+y_2}{2} \\ -5=\frac{-8+y_2}{2} \\ -5(2)=-8+y_2 \\ y_2=-10+8 \\ y_2=-2 \end{gathered}[/tex]Hence, the coordinate of Q is (-4,-2).