Let's calculate the distance between F and G:
F=(-4,-2)
G=(2,-2)
[tex]d=\sqrt[]{(2-(-4))^2+(-2-(-2))^2}=\sqrt[]{36}=6[/tex]
The distance between M and P is half the distance between F and G, so:
[tex]\frac{d}{2}=3[/tex]
The coordinates of P are:
P=(2,-8)
and
M=(x,-8)
So:
[tex]\begin{gathered} 3=\sqrt[]{(x-2)^2+\mleft(-8-\mleft(-8\mright)\mright)^2} \\ 3=x-2 \\ \text{solving for x:} \\ 3+2=x \\ 5=x \\ x=\pm5 \\ \end{gathered}[/tex]
Since M is in the 3rd quadrant:
M= (-5,-8)
----------------------------------------------
Let:
(x1,y1)=(-2,1)
(x2,y2)=(-5,4)
[tex]\begin{gathered} d=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ d=\sqrt[]{(-5-(-2))^2+(4-1)^2} \\ d=\sqrt[]{9+9}=\sqrt[]{18} \end{gathered}[/tex]
