If Vertices of a Triangle have Coordinates (-2,2) (3,2) GMAT Data Sufficiency

Question:  If Vertices of a triangle have coordinates (-2,2) (3,2) (x,y). What is the area of the triangle?

1. |y-2| = 1
2. Angle at the vertex (x,y) equals 90 degrees

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“Vertices of a triangle have coordinates (-2,2) (3,2) (x,y). What is the area of the triangle?”– is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

There is only one solution to this problem.

Given two points A (-2,2) and B (3,2).

Question asks to find the area of the triangle ABC, where C (x,y).

Look at the diagram below:

1. |y-2| = 1. Either y = 3 or y = 1, hence vertex C could be anywhere on the blue line y = 3 or anywhere on the red line y = 1. But in ANY case the area of ABC will be the same; area = \(\frac{1}{2}*Base*Height \) . So base AB = 5 and the height would be 1 for any point C (see two possible locations of C: C1, C2, the heights of ABC 1 and ABC 2 are the same and equal to 1). So, we have that area \(\frac{1}{2}*Base*Height=\frac{5}{2}\)

Hence this statement is Sufficient.

2. Angle of the vertex (x,y) equals to 90 degrees. This statement says that ABC is a right angled triangle with hypotenuse AB: consider AB to be the diameter of the circle. In this case C could be anywhere on the circle and it will be right angle (if the diameter of the circle is also the inscribed triangle’s side, then that triangle is a right triangle), thus the height of ABC will be different for different location of point C, resulting the different areas (see two possible locations of C: C3 and C4, heights of ABC 3 and ABC 4 are different).

Hence this statement is Not Sufficient.

Correct Answer: A

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