Answer:
The coordinates of B are (-8,-4)
Step-by-step explanation:
Midpoint of a segment
Given points A(xa,ya) and B(xb,yb), the coordinates of the midpoint M can be found knowing that:
[tex]\overline{AM}=\overline{MB}[/tex]
Applying that relation in both axes separately, we can write:
[tex]x_A-x_M=x_M-x_B[/tex]
[tex]y_A-y_M=y_M-y_B[/tex]
Knowing the coordinates of the midpoint and A, we can find the coordinates of the other extreme B solving both equations for the required variable:
[tex]x_B=2x_M-x_A[/tex]
[tex]y_B=2y_M-y_A[/tex]
Plugging in the known values:
[tex]x_B=2(-6)-(-4)=-12+4=-8[/tex]
[tex]y_B=2(-6)-(-8)=-12+8=-4[/tex]
The coordinates of B are (-8,-4)
