Please help!! ABCD is a trapezoid with bases AB and CD. Diagonals AC and BD intersect at point P and create similar triangles; AB:CD = 2:3

[kqtzs]

ABCD is a trapezoid with bases AB and CD.

Diagonals AC and BD intersect at point P and create similar triangles

АВР ~ ACP with ratio 2: 3 (i.e AB : CD is 2:3).

Point A is at (-6, -8), point C is at (9, 12), and point B is in quadrant II.

Find the intersection point P of the diagonals.

 

[The Highlander]

ABCD is a trapezoid with bases AB and CD.

Diagonals AC and BD intersect at point P and create similar triangles

АВР ~ ACP with ratio 2: 3 (i.e AB : CD is 2:3).

Point A is at (-6, -8), point C is at (9, 12), and point B is in quadrant II.

Find the intersection point P of the diagonals.

This is the second post of yours that I have looked at today.

In both posts all you have submitted is the question you have been given.

Do you expect someone here just to provide an answer to these questions for you?

This forum is here to help you to do your work, not to do your work for you.

You must submit your own efforts to answer a question when you post it so that we can see where you are having difficulty and offer the best advice to aid you in overcoming that difficulty.

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as explained here:-

READ BEFORE POSTING​

Please now share your work/thoughts about both the problems you have posted.

Thank you.

 

[khansaheb]

ABCD is a trapezoid with bases AB and CD.

Diagonals AC and BD intersect at point P and create similar triangles

АВР ~ ACP with ratio 2: 3 (i.e AB : CD is 2:3).

Point A is at (-6, -8), point C is at (9, 12), and point B is in quadrant II.

Find the intersection point P of the diagonals.

If I were to solve this problem,

first thing I would do is to sketch the parallelogram (ABCD) following the instruction​

Point A is at (-6, -8), point C is at (9, 12), and point B is in quadrant II​

Draw the diagonals AC and BD and locate point P.​

Post this sketch (a picture will do) in the forum - in hopes of "further help" - if you need it.

 

[The Highlander]

If I were to solve this problem,

first thing I would do is to sketch the parallelogram (ABCD) following the instruction​

Point A is at (-6, -8), point C is at (9, 12), and point B is in quadrant II​

Draw the diagonals AC and BD and locate point P.​

Post this sketch (a picture will do) in the forum - in hopes of "further help" - if you need it.

It strikes me that it would be rather difficult (if not well-nigh impossible) to make a useful sketch with just that information (otherwise I might have done it myself to give the OP a 'start').

I would expect that one would need to solve the problem first (or at least have a good idea of its final solution) before one might construct an appropriate and useful sketch of the parallelogram.

Perhaps someone who agrees with the idea of a (random?) sketch as a starting point might be good enough to provide one for the OP?

 

[Dr.Peterson]

Perhaps someone who agrees with the idea of a (random?) sketch as a starting point might be good enough to provide one for the OP?

Here is what I would mean by such a sketch:

​

A sketch is just an attempt to visualize the basic relationships stated in part of a problem, in order to understand what it is asking.

And in this case, what I have done reveals a flaw in what was stated: Since P is on diagonal AC, ACP can't be a triangle similar to ABP.

I would say that is very helpful!

We could make a good guess at what is intended, but if the typo is in the problem itself, rather than just in the copying, then it's significant.

It strikes me that it would be rather difficult (if not well-nigh impossible) to make a useful sketch with just that information (otherwise I might have done it myself to give the OP a 'start').

I would expect that one would need to solve the problem first (or at least have a good idea of its final solution) before one might construct an appropriate and useful sketch of the parallelogram.

Again, a sketch is not meant to be an accurate representation of the final solution. It doesn't have to be to scale. So you don't have to solve the problem first.

After straightening this out, I might make a sketch using the coordinates, in which I would still not be expecting accuracy. (In particular, I probably wouldn't worry about the ratio.) I would be looking for relationships.

 

[The Highlander]

Here is what I would mean by such a sketch:

View attachment 37888​

A sketch is just an attempt to visualize the basic relationships stated in part of a problem, in order to understand what it is asking.

And in this case, what I have done reveals a flaw in what was stated: Since P is on diagonal AC, ACP can't be a triangle similar to ABP.

I would say that is very helpful!

We could make a good guess at what is intended, but if the typo is in the problem itself, rather than just in the copying, then it's significant.


Again, a sketch is not meant to be an accurate representation of the final solution. It doesn't have to be to scale. So you don't have to solve the problem first.

After straightening this out, I might make a sketch using the coordinates, in which I would still not be expecting accuracy. (In particular, I probably wouldn't worry about the ratio.) I would be looking for relationships.

Unfortunately, your sketch doesn't conform to the conditions set out in the question as Point B lies to the left of Point C ("in quadrant II") at some unspecified location (so it might well serve to confuse the OP).

Of course I know that a sketch is not (necessarily) meant to be an accurate representation of a given situation and is just a useful starting point (springboard?) from which to begin to understand and thence answer a problem. I am, after all, the very person who is persistently telling new members to draw them!

The point I was making was that trying to make a sketch with the limited information suggested at Post #3 (ie: just two points and a vague location for a third) wasn't going to be very easy.

I made my own diagram (below) but in trying to construct it, after I had plotted the given Points A & C, I was forced to consider the other conditions specified in the question (which sides were the bases, their lengths ratio and what sensible, potential locations for D & B existed) before I was able to make any useful final construction and, in doing so, it then became obvious to me how to solve the problem and create a figure that satisfied all the conditions specified in the question.
(Except, ofc, that you're absolutely right that there is a typo (or copying) error in the third line of the question which should read: "АВР ~ DCP with ratio 2: 3 (i.e AB : CD is 2:3).".)

​

Edit: I also pointed out, at Post #2, that this OP is another one who just posts his questions (and expects answers or at least useful guidance to them) without submitting any attempts at the problems first (in breach of the forum rules).

Unfortunately, substantial help has now been provided to both his questions without any delay to see whther s/he would submit their own attempt first!

 

[Otis]

I didn't have any issue sketching ABCD. (My sketch matches Highlander's.) In fact, using graphing paper and a ruler made P's location a fairly-easy guess.

The misprinted similar triangle noted in post#6 would confuse anybody who considered it for drawing a sketch. (I didn't go that far, luckily.)

I agree with the correction:

AВР ~ DCP with ratio 2:3