Rectangle PQRS lies in the first quadrant...

[aljumaily.anas]

I recently came across a PS problem I could not solve. Namely, I cannot see how a rectangle can be drawn such that two of its points, which according to the description are not diagonal opposites, do not match in either X or Y coordinates.

Rectangle PQRS lies in the first quadrant of the xy-plane, with point P diagonally opposite point R and point Q diagonally opposite point S. The coordinates of points P and Q are (a + 2, 2a) and (a - 3, a), respectively. If Point R lies at (11, 2), what is the value of a?

[jnelson0612]

I recently came across a PS problem I could not solve. Namely, I cannot see how a rectangle can be drawn such that two of its points, which according to the description are not diagonal opposites, do not match in either X or Y coordinates.

Rectangle PQRS lies in the first quadrant of the xy-plane, with point P diagonally opposite point R and point Q diagonally opposite point S. The coordinates of points P and Q are (a + 2, 2a) and (a - 3, a), respectively. If Point R lies at (11, 2), what is the value of a?

We're happy to help, but what is the original source of this problem?

[aljumaily.anas]

It's from Knewton

[RonPurewal]

Per the forum rules, please post all answer choices that accompany this problem.

This is protocol anyway"”but it's especially important here, because backsolving is going to be a very viable alternative here.

Thanks.

[ralphh539]

I recently came across a PS problem I could not solve. Namely, I cannot see how a rectangle can be drawn such that two of its points, which according to the description are not diagonal opposites, do not match in either X or Y coordinates.

Rectangle PQRS lies in the first quadrant of the xy-plane, with point P diagonally opposite point R and point Q diagonally opposite point S. The coordinates of points P and Q are (a + 2, 2a) and (a - 3, a), respectively. If Point R lies at (11, 2), what is the value of a?

Is that a free source?

[tim]

I'd like to know this as well. It is important that we respect other companies' intellectual property rights and not pirate their questions on this forum.

[RonPurewal]

Well, the way we've traditionally run things around here is, basically, "Problems from a random source are fine, as long as we haven't been explicitly asked NOT to use that source". (Hence the list of banned sources.)

Knewton isn't in the list of banned sources, so, for now, the problem is fine.

But"”we still need the answer choices. It should be pretty straightforward to backsolve this problem (and much less straightforward to solve without the answer choices), so it would be a disservice to present this problem without the choices.

Thanks.

[tim]

Thanks for clarifying that, Ron! And yes, we still need answer choices.