Final answer:
To graph point E on segment CD such that CE:DE is 5:2, draw line CD, choose any point for E, measure segments CE as 5 units and DE as 2 units, ensuring the ratio is correct, and label point E.
Step-by-step explanation:
To graph the point E on line segment CD based on the given ratio CE:DE = 5:2, we first need to understand that the ratio represents the relative lengths of segments CE and DE with respect to each other. This information implies that for every 5 parts that CE measures, DE measures 2 parts. To graph this, we can take the following steps:
- Draw line segment CD on a coordinate plane or a piece of graph paper.
- Select any point along CD to be point E, the point of division. Do not mark it yet.
- From the chosen point E, measure out CE as 5 units of any chosen length, and mark this point on the line.
- From the chosen point E, measure out DE as 2 units of the same chosen length in the opposite direction, and mark this point on the line.
- Verify that the ratio CE:DE is exactly 5:2 by comparing the lengths of both segments.
- Clearly label point E on your graph.
The above method ensures that we respect the given ratio and graph point E accurately. Remember, the actual lengths you choose for the units do not matter as long as the ratio is correct.