Point C is the middle of segment AB. Find the coordinates of point B if A (-3, -2), C (1, -3).

It is known from the condition that point C is the midpoint of the segment AB. And we need to find the coordinates of point B, if it is known that the coordinates of points A (-3; -2) and C (1; -3).

Let’s start by writing the ratio:

c = (a + b) / 2.

For the coordinates of point C, we can write the following equalities:

xc = (xa + xb) / 2;

2 = (-4 + xb) / 2;

4 = -4 + xb;

xb = 8.

We do the same with the ordinate of point B.

yc = (ya + yb) / 2;

1 = (3 + yb) / 2;

2 = 3 + yb;

yb = 2 – 3;

yb = -1.

That is, point B has coordinates xb = 8; yb = -1 or B (8; -1).