More elegant solution to this 'solve for coordinates' question?

[dante92]

Hi all,

My first post here, sorry in advance if this is in the wrong section. Trying to help out my niece with her homework, so I appreciate in advance if anyone can lend a hand where I could not.
Question as below, and my initial workings before I got stumped.





And then that's where I got stuck.
While I know you could reasonably assume A and C's X coordinates as 10 and 50 respectively, and their Y coordinates as 10 and 30 respectively (and then work from there), my niece's textbook states that there are multiple reasonable solutions to this question.

Ultimately I wonder if I'm just wandering down a wayward road to nowhere or if there is actually an elegant algebraic answer.
Once again, sorry if this is in the wrong section or if this is formatted incorrectly. Thank you in advance to anyone who can help.

 

[Deleted member 4993]

Hi all,

My first post here, sorry in advance if this is in the wrong section. Trying to help out my niece with her homework, so I appreciate in advance if anyone can lend a hand where I could not.
Question as below, and my initial workings before I got stumped.

View attachment 33467

View attachment 33468

And then that's where I got stuck.
While I know you could reasonably assume A and C's X coordinates as 10 and 50 respectively, and their Y coordinates as 10 and 30 respectively (and then work from there), my niece's textbook states that there are multiple reasonable solutions to this question.

Ultimately I wonder if I'm just wandering down a wayward road to nowhere or if there is actually an elegant algebraic answer.
Once again, sorry if this is in the wrong section or if this is formatted incorrectly. Thank you in advance to anyone who can help.

I would start with assuming AD = 10 and AB = 20

Then coordinate of A would be (20,15).....continue...

Since only "possible" answers are required this process could be faster.

 

[Dr.Peterson]

Hi all,

My first post here, sorry in advance if this is in the wrong section. Trying to help out my niece with her homework, so I appreciate in advance if anyone can lend a hand where I could not.
Question as below, and my initial workings before I got stumped.

View attachment 33467

View attachment 33468

And then that's where I got stuck.
While I know you could reasonably assume A and C's X coordinates as 10 and 50 respectively, and their Y coordinates as 10 and 30 respectively (and then work from there), my niece's textbook states that there are multiple reasonable solutions to this question.

Ultimately I wonder if I'm just wandering down a wayward road to nowhere or if there is actually an elegant algebraic answer.
Once again, sorry if this is in the wrong section or if this is formatted incorrectly. Thank you in advance to anyone who can help.

They aren't asking you to find all solutions, or even more than one, so you are expected to just pick some coordinates. What you suggest initially would be fine. That is what your niece should do. And if she wants; she might pick a second pair for A to get a second answer. (What if A were (0,0)? Could that work?)

If you are just making this an extra challenge for yourself to find a general formula for all solutions, then you might just specify [imath]A=(x_A,?)[/imath] and work out the other coordinates from that. (Or it might be a little easier to take the y-coordinate of A as given rather than x. Or you might start with the height of the rectangle being h, and work out the coordinates from that.)

One approach would be to find the height and width of the rectangle in terms of the parameter [imath]x_A[/imath], by comparing the latter to E. Or you could do something similar to what you tried to find the other x coordinate and the other y coordinate.

I also think that working through a specific example, from start to finish, would be good practice for the general case. You'll need to think through and write out the reasoning behind the assumptions you stated, which presumably have a lot of good thinking behind them. (Unless its mostly a good guess.) How did you choose 10, 50, 10, and 30?

But let your niece do what she wants to do, with minimal direction.