P and Q Given, Find R so that RQ = 1/4PQ

[SaltyPoro]

(I'm sorry if this is the wrong section to be posting this.)

I stumbled across a question on my worksheet which I have no idea how to do, the only thing on the worksheet explaining anything is the basic formula for finding the midpoint of 2 points.
The question goes: The coordinates of P and Q are (-8,3) and (4,-5) respectively; determine the coordinates of the point R so that RQ = 1/4PQ.
Please go through the working out and explain briefly how it was done, thank you in advance .
PS: I'm only in year 8

 

[Deleted member 4993]

(I'm sorry if this is the wrong section to be posting this.)

I stumbled across a question on my worksheet which I have no idea how to do, the only thing on the worksheet explaining anything is the basic formula for finding the midpoint of 2 points.
The question goes: The coordinates of P and Q are (-8,3) and (4,-5) respectively; determine the coordinates of the point R so that RQ = 1/4PQ.
Please go through the working out and explain briefly how it was done, thank you in advance .
PS: I'm only in year 8

Did you approximately plot these points (preferably on a graph paper)?

 

[SaltyPoro]

I just realised how stupid I am, didn't think it was so simple to get the answer haha. All I had to do was apply the midpoint formula twice to find 1/4 of PQ.
(I posted this in the wrong section, oops.)

 

[mmm4444bot]

All I had to do was apply the midpoint formula twice to find 1/4 of PQ.

Another way: use the distance formula to get 4·√13 units for the length of PQ, and then divide by four (to get √13 as one-fourth the distance).

Were you told that point R is located on the line segment connecting points P and Q?

If not, I'm letting you know that an infinite number of possible locations exist for point R; each of them is √13 units away from Q. :cool:

 

[SaltyPoro]

Another way: use the distance formula to get 4·√13 units for the length of PQ, and then divide by four (to get √13 as one-fourth the distance).

Were you told that point R is located on the line segment connecting points P and Q?

If not, I'm letting you know that an infinite number of possible locations exist for point R; each of them is √13 units away from Q. :cool:

Wait a minute.
I tried the method you suggested above the first time I done it but I thought I was incorrect.
The question is exactly as above so I don't think it said anything about being on the line segment.

 

[mmm4444bot]

… I don't think it said anything about being on the line segment.

Then the coordinates of any point on a circle with radius √13 centered at point Q will do. :wink:

Have you studied equations of circles, yet?

If not, you'll probably want to report one of the two points on the line passing through points P and Q.