What is the area of the triangle ?

[goelmohit2002]

Sorry...I am not able to attach the figure....please refer to the figure at the following link....

http://www.beatthegmat.com/what-is-the- ... tml#190846

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The figure shows a right triangle in xy plane. If coordinate of A is (-15, 10), what is the area of triangle ABC ?
1) The coorinate of point B is (25, 25)
2) The coordinate of point C is (25,10)

OA = C. Can someone please tell can't we assume the right angle is at angle C. From figure it does not seem possible to have right angle anywhere else.

[kolla.cheerful]

The triangle is right angled at c.The area of the triangle will be 1/2*40*15=300units.Hence C

[goelmohit2002]

The triangle is right angled at c.The area of the triangle will be 1/2*40*15=300units.Hence C

if u assume that triangle is right angled at C...then I guess answer should be A alone.

since using 1 alone we can get the base and height length....

Please correct me if I am wrong.

But Please tell why angle C should be assumed to be 90...nowhere in the question it is mentioned to be 90

[RonPurewal]

whoa there people.

EVEN IF we assume that the right angle is at C, statement 1 is STILL not good enough to determine the area of the triangle.

even if we know that C is the right angle, all we know is the location of the hypotenuse. we have no reason to assume that the other two sides are parallel to the x- and y-axes.

there are LOTS of different right triangles with this side as hypotenuse - try drawing some. they'll have areas ranging all the way from approximately 0 (if point C is very close to A or B) to a maximum value (if the triangle is 45-45-90).

so yeah, that's still not sufficient. therefore, the issue of whether the right angle is located at C is immaterial; statement 1 is insufficient whether this is necessarily true or not.

--

by the way, this question creates a REALLY bad precedent for the actual test.

in this problem, statements (1) and (2) together HAND YOU ALL THE INFORMATION IN THE PROBLEM, WITH NO WORK AT ALL. i.e., if you have BOTH of these statements, then you have all 3 points of the triangle, and there is nothing left to find out.

on the REAL exam, on problems like this (when the two statements together just hand you everything you need), the answer is very, very rarely C. (this is what we call a "c trap".)

if you have the 12th edition og, check out problems #60, 107, 136, 154, and 173 in the data sufficiency question. all are C traps. none have C as the correct answer.

[goelmohit2002]

whoa there people.

EVEN IF we assume that the right angle is at C, statement 1 is STILL not good enough to determine the area of the triangle.

even if we know that C is the right angle, all we know is the location of the hypotenuse. we have no reason to assume that the other two sides are parallel to the x- and y-axes.

there are LOTS of different right triangles with this side as hypotenuse - try drawing some. they'll have areas ranging all the way from approximately 0 (if point C is very close to A or B) to a maximum value (if the triangle is 45-45-90).

so yeah, that's still not sufficient. therefore, the issue of whether the right angle is located at C is immaterial; statement 1 is insufficient whether this is necessarily true or not.

--

by the way, this question creates a REALLY bad precedent for the actual test.

in this problem, statements (1) and (2) together HAND YOU ALL THE INFORMATION IN THE PROBLEM, WITH NO WORK AT ALL. i.e., if you have BOTH of these statements, then you have all 3 points of the triangle, and there is nothing left to find out.

on the REAL exam, on problems like this (when the two statements together just hand you everything you need), the answer is very, very rarely C. (this is what we call a "c trap".)

if you have the 12th edition og, check out problems #60, 107, 136, 154, and 173 in the data sufficiency question. all are C traps. none have C as the correct answer.

Hi Ron,

Thanks !!!

What about statement 2 alone....is that sufficient ?

Thanks
Mohit

[goelmohit2002]

we have no reason to assume that the other two sides are parallel to the x- and y-axes.

there are LOTS of different right triangles with this side as hypotenuse - try drawing some. they'll have areas ranging all the way from approximately 0 (if point C is very close to A or B) to a maximum value (if the triangle is 45-45-90).

so yeah, that's still not sufficient. therefore, the issue of whether the right angle is located at C is immaterial; statement 1 is insufficient whether this is necessarily true or not.

Awesome Ron !!!!

Thanks a lot....

[Ben Ku]

Statement (2) provides the same information as statement (1). It alone is insufficient.

We cannot find out the measure of any angle in a triangle unless we have the coordinates of all three vertices.