In the coordinate plane, a triangle ABC has 3 points A(-1,0), B(1,0),

Question

In the coordinate plane, a triangle ABC has 3 points A(-1,0), B(1,0), and C(m,n). What is the area of the triangle ABC?

1) m=2
2) n=2

Bunuel · Answer

This is a copy of the following question: https://gmatclub.com/forum/in-the-coord ... 49146.html

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 that equal number of variables and independent equations ensures a solution.
The first step of VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations.
We can consider AB as the base and the y-coordinate n of the point C as another point of the triangle, and |n| is its height.
Thus, its area is (1/2)*2*|n| = |n|.

Hence, only condition 2) is sufficient.

Therefore, B is the answer.

Answer: B

Mick1005 · Answer

Hi,
Can you explain why are you taking the triangle as right angled triangle?
It could be acute or obtuse also for example coordinates 3,2 will give obtuse triangle and in the question it is not mentioned that it is a right angled triangle.
Thats why I had marked C. Didnt understand why we should take it as right angled triangle.

MathRevolution · Answer

Since A(-1,0), B(1,0) and AB is parallel to the x-axies, when we know y-coordinate of the point C, we identify the height of the triangle with the base AB.
We don't need to consider a right triangle in this case.

GMATSkilled · Answer

We know AB. So let AB be the base of the triangle.
Now we need to find the height of the triangle... Y = K is a line parallel to x-axis.
The distance between this line and the x axis will always be the same as its parallel. Hence irrespective of the x axis or the point, the height of the triangle formed with any point in this line will be have the same area.
Option B gives us the solution Y = 3

Sent from my iPhone using GMAT Club Forum

bumpbot · Answer

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In the coordinate plane, a triangle ABC has 3 points A(-1,0), B(1,0),

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In the coordinate plane, a triangle ABC has 3 points A(-1,0), B(1,0),

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