A rectangle is plotted on the standard coordinate plane,

Question

A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices?

(1) The length of the diagonal is 13 units.

(2) The distance between the origin and one of the other vertices is 5 units.

JenniferClopton · Answer

***OA INCORRECTLY LISTED AS "A." CORRECT ANSWER IS "E" AS CONFIRMED BELOW.***

I chose E. Does "standard coordinate plane" imply Q1? If not, couldn't the rectangle lie in either Q1 or Q4?

Furthermore, if Q1 is implied, then why is the answer not D?

Bunuel · Answer

So we have two vertices O(0,0) and B(12,0). First note that OA may be either one of the sides or a diagonal.

(1) The length of the diagonal is 13 units --> clearly OA is not a diagonal, so it's one of the sides. Now, if we take the length of the other side to be equal to x then we'll have x^2+12^2=13^2 --> x=5. But from this we can not get the coordinates of the other vertices. As you correctly noted rectangle can be in I quadrant with the other two vertices at (0, 5) and (12, 5) OR in IV quadrant with the other two vertices at (0, -5) and (12, -5). Not sufficient.

(2) The distance between the origin and one of the other vertices is 5 units. Clearly insufficient.

(1)+(2) Still two answers are possible: (0, 5) and (12, 5) OR (0, -5) and (12, -5). Not sufficient.

Answer: E.

JenniferClopton · Answer

OK, while I had not considered the additional possibilities of a rotated position, I concur that the answer is E.

Unless I have missed something, this question is wrong?

Are we absolutely sure that Q1 is not implied?

Bunuel · Answer

Yes, I think answer A is wrong. Can you please post OE for it to see where they went wrong?

muralimba · Answer

The answr must be "E". Not "A". Please post the correct OA. Here is the simle explanation. Just imagine the rectangle in the co-ordinate place. You get the answer. No need to use any calculations/values. The below shows the picture with two rectangles, one in red and another in green, which can be drawn for statement given and which have different co-ordinates except the two given in the question. rectangles.JPG Regards, Murali. Kudos?

jaxis · Answer

even if it is implied the answer shud be D not A becoz 5 cant be the diagonal as one side is already 12 and the diagonal will be greater than both sides.

Cheers,
Jaxis.

JenniferClopton · Answer

The answer has been corrected above. Also, for any Grockit subscribers, I have reported the error to the Grockit support team.

anish319 · Answer

wow good question i didnt see the other quadrant possibility.

hamzakb · Answer

How can a rectangle have two unequal parallel sides (12 & 13)?

beats me

Bunuel · Answer

It cannot. Where in my solution is written this?

hamzakb · Answer

(1) The length of the diagonal is 13 units.

(2) The distance between the origin and one of the other vertices is 5 units.

So we have two vertices O(0,0) and B(12,0). First note that OA may be either one of the sides or a diagonal.

(1) The length of the diagonal is 13 units --> clearly OA is not a diagonal, so it's one of the sides. Now, if we take the length of the other side to be equal to x then we'll have x^2+12^2=13^2 --> x=5. But from this we can not get the coordinates of the other vertices. As you correctly noted rectangle can be in I quadrant with the other two vertices at (0, 5) and (12, 5) OR in IV quadrant with the other two vertices at (0, -5) and (12, -5). Not sufficient.

(2) The distance between the origin and one of the other vertices is 5 units. Clearly insufficient.

(1)+(2) Still two answers are possible: (0, 5) and (12, 5) OR (0, -5) and (12, -5). Not sufficient.

Answer: E.

You say clearly OA is not a diagonal, it is one of the side. I think you are mentioning to two sets of parallel lines having length 12 & 13?

Also, how can 13 not be a diagonal, given that it has been explicitly mentioned in the question that it IS a diagonal.

Bunuel · Answer

You are not reading the question and the solution carefully. Also, with geometry and coordinate geometry question it's always a good idea to make a sketch: Untitled.png OA is NOT the diagonal it's one of the sides, diagonal = 13. Two possible rectangles. Hope it's clear now.

hamzakb · Answer

I get it. I didn't understand properly before.

Thanks a lot!! Your posts are the most helpful I've found on the net

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

A rectangle is plotted on the standard coordinate plane, with vertices at the origin and (12,0). What are the coordinates of the other two vertices?

(1) The length of the diagonal is 13 units.

(2) The distance between the origin and one of the other vertices is 5 units.

There is one variable (b), and 2 equations are given; the answer is likely to be (D).
From condition 1, b=5, -5. So this is an insufficient condition as it does not give a unique answer.
condition 2, similarly, gives b=5, -5, so this is also insufficient for the same reason.
Even if we combine the 2 conditions, b=5,-5, so as a whole, they are insufficient, so the answer is going to be (E).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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A rectangle is plotted on the standard coordinate plane,

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A rectangle is plotted on the standard coordinate plane,

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