In the rectangular coordinate system above, is ABCD a square?

Question

https://gmatclub.com/forum/download/file.php?id=46743 In the rectangular coordinate system above, is ABCD a square? (1) Both Points C and D have y-coordinates of 3. (2) ∠ABD = 45° 2019-03-05_1602.png

Chethan92 · Answer

From S1:

CD is a straight line.
No info about A and B.
Insufficient.

From S2:

Angle ABD is 45.
Again no extra info.
Insufficient.

Combining both: Still, angle DBC and Angle BAD are unknown.

E is the answer.

Archit3110 · Answer

for a square to be valid ; the distance between two points should be same and known
#1
y cordinate know .. x is not known
in sufficient
#2
∠ABD = 45°
not sufficeint and as other side angles not know

from 1&2
we cannot deduce anything in common to conclude its a square
IMOE

Sourav700 · Answer

Anyone with a better explanation for this question?

i understand the info provided are: DC is a straight line (can we assume it is equal and parallel to AB)
SECOND, one angle given is 45, again we assume each angle is 90?

I generally get stuck in such question, where there is a subtle hint of the figure being a rectangle, square, rhombus or a llgm.

IanStewart

IanStewart · Answer

No you shouldn't assume either of those things - you're not told they are true, and they can't be deduced from anything in the question.

We really don't have nearly enough information to conclude the shape is a square. One DS technique you can sometimes use in Geometry questions is to ask: how much freedom do I have to draw the diagram in different ways? Here, we can easily see that the diagram could be a square. But even if we first assume, for simplicity, that the slope of the line through the origin is 1, so that AB and CD are in fact parallel, we still have no idea where point A is. It could be miles off to the left, say, and angle CDA could be much bigger than 90 degrees. So we can draw the diagram in various ways, sometimes getting a square, sometimes not, and the answer is E.

And if you notice that you don't even know the slope of that line through the origin, you can find yet other ways to draw shapes that aren't squares.

Sourav700 · Answer

Thanks a ton  IanStewart .

Posted from my mobile device

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In the rectangular coordinate system above, is ABCD a square?

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In the rectangular coordinate system above, is ABCD a square?

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