Final answer:
To find OD in the parallelogram OABC, we use its properties to establish that OA = OC = x and AB = BC = y. Since M is the midpoint, OM = MC = x/2, and because BD = 3BC, OD = x + 3y.
Step-by-step explanation:
The question asks to find the length of OD in a parallelogram OABC where OA = x, AB = y, and BCD is a straight line with BD = 3BC. M is the midpoint of OC, indicating OM = MC.
To find OD, we can use the properties of a parallelogram that opposite sides are equal, so OA = OC = x, and AB = BC = y.
Since M is the midpoint of OC, OM = MC = x/2. Because BD = 3BC = 3y, OD, which is the sum of OC and CD, equals x + 3y.
Therefore, OD = x + 3y.