Question

The midpoint of AB is M(-6, -6). If the coordinates of A are (-4-8), what are

Answer 1

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:

$\overline{AM}=\overline{MB}$

Applying that relation in both axes separately, we can write:

$x_A-x_M=x_M-x_B$

$y_A-y_M=y_M-y_B$

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:

$x_B=2x_M-x_A$

$y_B=2y_M-y_A$

Plugging in the known values:

$x_B=2(-6)-(-4)=-12+4=-8$

$y_B=2(-6)-(-8)=-12+8=-4$

The coordinates of B are (-8,-4)