Final answer:
After analyzing the geometry of the triangle, DC should be 22 units and CM should be 11 units.
Step-by-step explanation:
The problem involves a triangle ADEF where D is a vertex, M is the midpoint of the side opposite to D, and C is the centroid of the triangle.
Since DM is given as 33 units, and the centroid (C) divides the median (DM) into two segments, where the segment attaching to the vertex (DC) is twice as long as the other segment (CM), we have the ratios 2:1. So, if DM is 33 units, DC must be 22 units, and CM must be 11 units, because DC is twice CM. This is not one of the options given, suggesting there may have been a typo in the multiple-choice options provided.
To find the lengths of DC and CM, we can use the properties of a centroid and a midpoint. In a triangle, the centroid divides the medians into segments with a ratio of 2:1.
This means that DC is double the length of MC. Since DM is given as 33 units, we can divide it into segments of 2:1 to find that DC = 22 units and MC = 11 units. Therefore, the correct answer is A. DC = 33 units, CM = 16.5 units