finding an endpoint

Question

Point C lies 5/6 of the way along line AB, closer to B than A. if the coordinates of Point a are (12,5) and the coordinates of Point C (9.5,-2.50, what are the coordinates of Point B.

Answer 1

A___________C__B

A=(12,5)

C=(9.5,-2.5)

B=(x,y)

if C is 5/6 of the way to B, then C is 1/6 of the way to A from B

first find the slope of AC   (y2-y1)/(x2-x1); the rise over the run

slope=(5-[-2.5])/(12-9.5)

slope=7.5/2.5

slope=3/1

again, C is 1/6 of the way to A from B

take 1/6 of the rise (3) of the slope; slope=rise/run

add this to y and you get -2.5

(1/6)*3+y=-2.5

3/6+y=-2.5

y=-2.5-0.5  (3/6)=0.5

y=-3

take 1/6 of the run (1) of the slope

add this to x and you get 9.5 (9.5 and -2.5 are the coordinates of C)

1/6+x=9.5

x=9.5-1/6

x=9 1/2-1/6

x=19/2-1/6

x=57/6-1/6

x=56/6

x=9 1/3

the coordinates of point B are(9 1/3, -3)

to check this find the slope with B and C and find the slope with B and A and you should get 3/1 both times

with B and C:

(-3-[-2.5])/9 1/3-9 1/2)

-0.5/(-1/6)

(1/2)/(1/6)=(1/2)(6/1)=3/1

with B and A:

(5-[-3])/(12-9 1/3)

8/(2 2/3)

8/(8/3)

(8)(3/8)=3/1

check !!