Points c, d, and e are collinear on ce, and cd: de = 3/5. c is located at (1,8), d is located at (4,5), and e is located at (x, y). what are the values of x and y

The point E is located at (9,0)

x=9, y=0

Step-by-step explanation:

we have that

Points C,D, and E are collinear on CE

Point D is between point C and point E

we know that

-----> equation A (by addition segment postulate)

------> equation B

the formula to calculate the distance between two points is equal to

Find the distance CD  

we have

C(1,8), D(4,5)

substitute in the formula

Find the distance DE

substitute the value of CD in the equation B and solve for DE

Find the distance CE

we have

substitute the values in the equation A

Applying the formula of distance CE

we have

C(1,8), E(x,y)    

substitute in the formula of distance

squared both sides

 -----> equation C

Applying the formula of distance DE

we have

D(4,5), E(x,y)    

substitute in the formula of distance

squared both sides

 -----> equation D

we have the system

 -----> equation C

 -----> equation D

Solve the system by graphing

The intersection point both graphs is the solution of the system

The solution is the point (9,0)

therefore

The point E is located at (9,0)

see the attached figure to better understand the problem