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Points P, R, M and S lie on the number line shown. The coor [#permalink]
26 Feb 2013, 07:31

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Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

(1) The coordinate of M is 1.5 (2) The coordinate of S is 6

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]
26 Feb 2013, 07:51

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This post received KUDOS

Expert's post

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

(1) The coordinate of M is 1.5 --> 1.5=(S+P)/2. We have 2 distinct linear equations (1.5=(S+P)/2 and S=-2P) with 2 unknowns, thus we can solve for both of them. Sufficient.

(2) The coordinate of S is 6 --> 6=-2P --> P=-3. Sufficient.

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]
26 Feb 2013, 08:13

Bunuel wrote:

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

Thanks!

Question tho, are you getting -P (because it's to the left of 0) by subtracting -P-R ---> -P-(0) = -P ?

Then isn't the distance between S and P ---> S-(-P) = S+P? _________________

If my post has contributed to your learning or teaching in any way, feel free to hit the kudos button ^_^

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]
26 Feb 2013, 09:01

Expert's post

DelSingh wrote:

Bunuel wrote:

Points P, R, M and S lie on the number line shown. The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S. If M is the midpoint of line segment PS, what is the coordinate of P?

The distance between P and R is 1/3 the distance between P and S --> -P=1/3*(S-P) (the distance between P and R=0 is -P and the distance between P and S is S-P) --> S=-2P. M is the midpoint of line segment PS --> M=(S+P)/2.

Thanks!

Question tho, are you getting -P (because it's to the left of 0) by subtracting -P-R ---> -P-(0) = -P ?

Then isn't the distance between S and P ---> S-(-P) = S+P?

Use numbers to test.

What is the distance between -3 and 0? It's 3. What is the distance between -3 and 6? It's 6-(-3)=9. _________________

Re: Points P, R, M and S lie on the number line shown. The coor [#permalink]
01 Jul 2014, 20:30

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