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

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