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If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.

Answer: D

Can you please explain statement one in more detail i.e. how area is same .

If vertices of a triangle are A (5, 0), B (x, y) and C (25, 0), what is the area of the triangle?

(1) |x| = y = 10

(2) x = |y| = 10

Given that vertices of a triangle are A (5, 0) and C (25, 0) =>Two vertices of the triangle are on x-axis =>Base = 20. Area of a triangle = 1/2*(base)*(height) Since, base is given, area of the triangle can be found if any of the following statement uniquely provide height of the triangle.

Statement 1: |x| = y = 10 Or, x point lies on the line y=10 => height of the triangle=10 => sufficient.....(B)(C)(E) Statement 2: x = |y| = 10 Or, y point lies on the line x=10 => height of the triangle =10 => sufficient.....(A)(D)

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.

Answer: D

Can you please explain statement one in more detail i.e. how area is same .

Look at the diagram below:

Attachment:

Untitled.png

Notice that no matter where point B is (blue or green dot) the area of the triangle would be the same, because the base (red segment) and the height would be the same.

>> !!!

You do not have the required permissions to view the files attached to this post.

Please correct me, if my reasoning for the above question is wrong.

The two specified co-ordinates will be on X-Axis. (1) Y = 10 and the co-ordinate of x can be either 10 or -10, but in both the cases, X will lie on a straight line that is parallel to X Axis, thus we can use the Triangle area concept that if two points of a triangle lie on a line then the all the triangles formed with the third point on the parallel line will have the same area.

(2) The same concept can be used here. Though in this case, it is visible that the two triangles formed will be mirror image of each other, thus even in this case the area can be known.

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.

Answer: D

Hi Bunuel,

Is it the value of x that doesnt affect the area of the triangle not the value of y?

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.

Answer: D

Hi Bunuel,

Is it the value of x that doesnt affect the area of the triangle not the value of y?

For the first statement it's the value of x and for the second one it's the value of y.
_________________

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.

Answer: D

Can you please explain statement one in more detail i.e. how area is same .

Look at the diagram below:

Attachment:

Untitled.png

Notice that no matter where point B is (blue or green dot) the area of the triangle would be the same, because the base (red segment) and the height would be the same.

Dear Bunuel, that is the same what i am draw and that is what i am ask for. In the green triangle I need to

understand which side is the height and how it equal to 10.I really confused
_________________

Statement 1: If \(|x| = y = 10\), \(y\) is 10 but \(x\) could be -10 or 10. The area is same for \(x = 10\) and \(x = -10\). This is sufficient to answer the question.

Statement 2: If \(x = |y| = 10\), \(x = 10\) but \(y\) could be 10 or -10 but different value of \(y\) does not affect the area of the triangle. This statement is also sufficient to answer the question.

Answer: D

Look at the diagram below:

Attachment:

Untitled.png

Notice that no matter where point B is (blue or green dot) the area of the triangle would be the same, because the base (red segment) and the height would be the same.

Dear Bunuel, that is the same what i am draw and that is what i am ask for. In the green triangle I need to

understand which side is the height and how it equal to 10.I really confused

I think that you really need to brush up fundamentals on geometry.

>> !!!

You do not have the required permissions to view the files attached to this post.

Height of triangle is to be drawn perpendicular to base from third co ordinate. In this case base has to be extended towards left where perpendicular from third co ordinate meets the base. Hope this would make little bit clear

I am also trying to understand, whether Hero's formula or Deterinant method to calculate triangle area can also help proove that the sign of x or y do not matter.

I don't agree with the explanation. USING STATEMENT 1 WE WILL GET 2 COORDINATES BUT AREA USING THE 2 COORDINATES WILL BE DIFFERENT. BUT USING STATEMENT 2 THE AREA OF THE TRIANGLE USING BOTH THE COORDINATES WILL BE SAME.

I don't agree with the explanation. USING STATEMENT 1 WE WILL GET 2 COORDINATES BUT AREA USING THE 2 COORDINATES WILL BE DIFFERENT. BUT USING STATEMENT 2 THE AREA OF THE TRIANGLE USING BOTH THE COORDINATES WILL BE SAME.

SO THE ANSWER SHOULD BE B

First of all, please turn of caps lock when posting. Next, please read the whole discussion before posting. For example, check this post: https://gmatclub.com/forum/d01-183495.html#p1481313 _________________