Coordinate Geometry

[HHeLiBeB]

Hi! I have no idea about this question

P and Q are points on a line segment with end point A(1,8) and B(10,5). If P and Q divide AB into three equal parts such that AP=PQ=QB, find the coordinates of P and Q.

thank you

 

[stapel]

P and Q are points on a line segment with end point A(1,8) and B(10,5). If P and Q divide AB into three equal parts such that AP=PQ=QB, find the coordinates of P and Q.

Method 1: Find the length of the entire segment, using the Distance Formula. (link)

Divide this by 3 to obtain the lengths of the "three equal parts".

Find the slope of the line containing the segment. (link)

Create the equation of the line containing the segment. (link)

Plug an endpoint and the generic form into the Distance Formula, set the distance equal to one-third of the total length, and solve. Pick the valid x-value, and back-solve for the corresponding y-value. Repeat using the other endpoint to find the other one-third point.

Method 2: You would use the Midpoint Formula (link) to find the point the splits the segment into two equal pieces. How might you adjust that method in order to find the points that split into thirds?

The second method is probably the easier one.

 

[pka]

P and Q are points on a line segment with end point A(1,8) and B(10,5). If P and Q divide AB into three equal parts such that AP=PQ=QB, find the coordinates of P and Q.

Here is a completely different way to do it.
Note that \(\displaystyle B-A=(9,-3) \) so the line segment is \(\displaystyle \overline{AB}=(1+9t,8-3t) \).
[\(\displaystyle t=0 \) we get \(\displaystyle A \), \(\displaystyle t=1 \) we get \(\displaystyle B \).

Now let \(\displaystyle t=\frac{1}{3}\) to get \(\displaystyle P \) and let \(\displaystyle t=\frac{2}{3}\) to get \(\displaystyle Q \).

You should get \(\displaystyle (4,7)~\&~(7,6) \).

 

[lookagain]

... A(1,8) and B(10,5). If P and Q divide AB into three equal parts such that AP=PQ=QB, find the coordinates of P and Q.

- - - - - - - - - - - - - - - - - - - - - - - - - - - --- - - - - -


Find exactly two arithmetic terms between 1 and 10.


1, 4, 7, 10



Find exactly two arithmetic terms between 8 and 5.

8, 7, 6, 5



So, the coordinates of P and Q are (4, 7) and (7, 6), respectively.

 

[pka]

the student is evidently being introduced to to the
distance formula along with right triangles.

Dennis, just where does it say that?

 

[mmm4444bot]

Please do not post answers soon after a tutor has provided guidance. Let's give the student an opportunity to try. :cool:

 

[jonah2.0]

Warning: Beer soaked ramblings follow.

Hi! I have no idea ...

Top Ten reasons reasons given in asking for help:
10. No idea how to solve this (or some other variant of this much used line; it could be number one).
9. ???

 

[HHeLiBeB]

Thank you! You guys are so helpful
I have just known that there are so many ways to solve this question.;-) Math is amazing and sometimes I get unexpected answer from experts like you guys:cool:
And I think I get the most suitable way to solve this from Stapel but I'll still try my best to understand other methods
Actually, I had tried to use distance formula to find AB but later I got stuck on dividing by 3 since the answer is 9.4868...so I failed and skipped this method.:lol:
Yep, Stapel. Method 2 is the easiest and I finally use mid-pt formula and distance formula.

 

[Ishuda]

...

Btw, Subhotosh stated a few days ago that giving a solution
in full is ok after 24 hours. Was he serious?

I haven't seen that but I would think maybe a bit longer, say 48 hrs.

 

[mmm4444bot]

Subhotosh stated a few days ago that giving a solution
in full is ok after 24 hours. Was he serious?

I have not see that post, but it's a change from his prior statement (about two years ago) of five days. (If memory serves, I wrote 'one week' back then.)

There are differences between moderators, but I would agree that answers definitely ought not to be posted within 24 hours.

Cheers :cool: