Answer:
CD: y - 3 = (-3/1)(x - 7).
DA: y - 0 = (9/5)(x - 8).
Explanation:
Since AB and BC are sides of the parallelogram, you can determine the vectors representing these sides and then use those vectors to find the equations of the other two sides.
Find the vector AB:
Vector AB is the difference between the coordinates of point B and point A:
AB = OB - OA
AB = (6 - 0, 6 - 3) = (6, 3).
Find the vector BC:
Vector BC is the difference between the coordinates of point C and point B:
BC = OC - OA
BC = (7 - 6, 3 - 6) = (1, -3).
To find the equations of the other two sides, you can use these vectors as follows:
Equation of the side CD (opposite to AB):
Point D is the endpoint of CD, and you can find it by adding vector BC to point C:
D = (7 + 1, 3 - 3) = (8, 0).
Now, you can use the point-slope form of the equation of a line to find the equation of CD, using points C and D:
CD: y - 3 = (-3/1)(x - 7).
Equation of the side DA (opposite to BC):
Point A is the endpoint of DA, and you can find it by subtracting vector BC from point B:
A = (6 - 1, 6 + 3) = (5, 9).
Use the point-slope form of the equation of a line to find the equation of DA, using points D and A:
DA: y - 0 = (9/5)(x - 8).
Now you have the equations of all four sides of the parallelogram:
AB: y - 3 = (3/6)(x - 0).
BC: y - 6 = (-3/1)(x - 6).
CD: y - 3 = (-3/1)(x - 7).
DA: y - 0 = (9/5)(x - 8).