The coordinates of point B are (6, 3).
The coordinates of point C are (2, 4).
The solution to the parallelogram problem:
Given:
Coordinates of point A = (4, 7)
x = 6
y = 3
Steps:
To find the coordinates of point B:
Since ABCD is a parallelogram, opposite sides are parallel and congruent. This means that the vector from A to B is equal to the vector from C to D. Therefore, we can find the coordinates of point B by adding the vector from A to B to the coordinates of point A.
Vector from A to B = (x - 4, y - 7)
Coordinates of point B = (4 + x - 4, 7 + y - 7)
Coordinates of point B = (x, y)
To find the coordinates of point C:
Since ABCD is a parallelogram, opposite angles are congruent. This means that angle ABC is equal to angle ADC. Therefore, we can find the coordinates of point C by rotating the vector from A to B by 180 degrees.
Rotated vector from A to B = (-x, -y)
Coordinates of point C = (4 - x, 7 - y)
Answers:
The coordinates of point B are (6, 3).
The coordinates of point C are (2, 4).