I am having problems with the following On a number line if the endpoint of FG are -3 and 9, what coordinate of point P partitions the segment at a ratio of 2:1

Question

______________________

-3 -2 -1 0 1 2 3 4 5 6 7 8 9

Answer 1

I will assume point F is at -3 and point G is at 9

 

The length of your segment FG is the distance from

-3 to 9 which is 12. 

 

To divide FG into segments with a ration of 2:1 let's look

at simply splitting the segment into 3 equal parts first..

 

Since FG has a length of 12, then 1/3 of FG would have 

a length of 4  .... (1/3)(12)=4

 

2/3 would have a length of 8 ...  

 

Starting at the left end which is -3 ... count 8 points to

the right.  This puts us at point P = 5

 

FP = 8

PG = 4

 

FP:PG = 8:4 = 2:1

 

Note:  Alternatively we could split the other direction and

move backwards 8 spots from 9 putting point P at 1.

 

Answer 2

Cutting a segment in the ratio 2:1 means to cut it into three parts (2 + 1) and give two parts to one partition and one part to the other partition.

The distance from -3 to 9 is 12. 12 /3 = 4.

So 8 (2 x 4) goes to one partition and 4 goes to the other.

-3 + 8 = 5, and 5 + 4 = 9

The coordinate is 5.

 

Or

-3 + 4 = 1, 1 + 8 = 9

The coordinate could also be 1.