The parallelogram ABCD contains all neighboring vertices A (-4; 4) B (2; 8) and the point of intersection

| September 23, 2021 | education

The parallelogram ABCD contains all neighboring vertices A (-4; 4) B (2; 8) and the point of intersection of its diagonals E (2; 2). Find the coordinates of its vertices C and D.

The intersection point E of the parallelogram diagonals is the point at which the diagonals bisect each other. The coordinates of the point dividing any segment in half are equal to the average value of the same coordinates of the ends of the segment (diagonal):

Diagonal midpoint AC:

XE = (XA + XC) / 2;
YE = (YA + YC) / 2.

Diagonal midpoint BD:

XE = (XB + XD) / 2;
YE = (YB + YD) / 2.

From the first pair of equalities we find the coordinates of m. C:

XC = 2XE – XA = 4 – (-4) = 8;

YC = 2YE – YA = 4 – 4 = 0.

From the second pair of equalities we find the coordinates of point D:

XD = 2XE – XB = 4 – 2 = 2;

YD = 2YE – YB = 4 – 8 = -4.

Answer: C (8; 0), D (2, -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.