Line AC is 13 units long. Use coordinate algebra to locate a point E on Line AC such that the ratio of AE to EC is equal to the ratio of AD to DB which is 0.6. Show how you derived your answer. (Hine: Let x and AC - x represent the two line segments that make up Line AC
Accepted Solution
A:
Refer to the diagram shown below.
The length of AC = 13 (given).
Let the length of AE = x. Then the length of EC = 13 x.
The ratio of AE to EC is 0.6. Therefore [tex] \frac{x}{13-x} =0.6[/tex] Cross multiply. x = 0.6(13 - x) x = 7.8 - 0.6x 1.6x = 7.8 x = 4.875
That is, AC = 4.875 EC = 13 -x = 13 - 4.875 = 8.125
Answer: E is located on AC such that AC = 4.875 EC = 8.125