Points A (4; -1), B (2; -4), C (0; -1) are the vertices of triangle ABC. Considering points A, B, C

Points A (4; -1), B (2; -4), C (0; -1) are the vertices of triangle ABC. Considering points A, B, C as the vertices of parallelogram ABCD, find the coordinates of vertex D.

It is known from the condition that the points with coordinates A (4; -1), B (2; -4), C (0; -1) are the vertices of the triangle ABC. We need, considering the data points A, B, C as the vertices of the parallelogram ABCD, find the coordinates of the vertex of the parallelogram D.

We will start by finding the coordinates of the midpoint of the segment AC.

We denote the midpoint of the segment O (x; y),

We are looking for coordinates using the formula:

O ((xa + xb) / 2; (ya + yb) / 2);

O ((4 + 0) / 2; (-1 – 1) / 2);

O (2; -1).

As a result, we got the coordinates of points B (2; -4), D (x; y) and O (2; -1) – the middle of the segment BD.

We are looking for the coordinates of point D:

2 = (x + 2) / 2;

x + 2 = 4;

x = 2;

-1 = (y – 4) / 2;

y – 4 = -2;

y = 2.

Answer: D (2; 2).