# Three vertices of the parallelogram ABCD are given. Find its fourth vertex D if A (1; 3) B (2; 6) C (-3; 1)

By the property of the lengths of the sides of the parallelogram: AC = BD and these sides are parallel.

Hence, to find the coordinates of the point D, it is necessary to find the length of the segment AC and equate it to BD. Formula for finding the length of a segment:

(x2 – x1) ² + (y2 – y1) ² = d²;

where:

d is the length of the segment.

x, y – corresponding coordinates.

AC length:

AC² = (-3 – 1) 2 + (1 – 3) 2 = 20;

AC = √20;

Side length BD:

BD² = (x2 – 2) ² + (y2 – 6) ²;

(x2 – 2) ² + (y2 – 6) ² = 20

From the condition of parallelism of the sides, we obtain that x2 = -2, and y2 = 4.

Answer: x2 = -2, y2 = 4. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.