Final answer:
BD is called a segment, with a scale factor of 0.75 from BD to AE. An equation to solve for x would typically involve a proportion or a linear equation based on given lengths or perimeters.
Step-by-step explanation:
Given point B is the midpoint of line segment AC and point D is the midpoint of line segment EC, part A of the question is asking what BD is called. BD is called a segment. Part B is asking for the scale factor between BD and AE. To determine this, we must recognize that since D is the midpoint of EC, ED is equal to half of EC, and since B is the midpoint of AC, AB is equal to half of AC. Therefore, if AC is the full length, BD (which consists of AB and half of EC) is three-quarters of the length of AE, and thus the scale factor is ¾ or 0.75.
For part C, to set up an equation to solve for x assuming x to be the length of a segment or a numeric value we need further information. Typically, if x represents the length of one of the segments, and we have information such as the lengths of other segments or perimeters, we could establish a proportion or a linear equation to solve for x.