Posted by **Anonymous** on Sunday, September 18, 2011 at 10:47pm.

points a b and c are collinear if the distance from point a to point b is 8 more than twice the distance from point b to point c and the length of segment ac is 5 times the length of segment of bc, how long is segment ac

- geometry -
**Reiny**, Monday, September 19, 2011 at 8:16am
Make a sketch.

From "length of segment ac is 5 times the length of segment of bc" it is clear that AC is the longer part.

So call the endpoints of your line A and C and place B between them (doesn't really have to be to scale)

label BC = x

then AC = 5x

and AB = 4x

then it said , " the distance from point a to point b is 8 more than twice the distance from point b to point c " or

AB = 2(BC) + 8

4x = 2x + 8

2x = 8

x = 4

then AC = 5x = 20

check:

By my definitions,

BC = 4

AC =20

AB = 16

is 16 equal to 8 more than 2x4 ? YES!

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