D01-34

Official Solution:


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

(1) \(|x| = y = 10\)

The above statement means that \(y\) is 10, but \(x\) can be either -10 or 10. Thus, the third vertex B can be either at (-10, 10) or (10, 10). Notice, however, that the area will be the same in either case. The base of the triangle, the red segment in the image below, will have a length of 20, and the height from B will be 10. Therefore, the area of the triangle will be \(\frac{1}{2}*20*10 = 100\). Sufficient.



(2) \(x = |y| = 10\)

The above statement means that \(x\) is 10, but \(y\) can be either -10 or 10. Thus, the third vertex B can be either at (10, 10) or (10, -10). Notice, however, that the area will be the same in either case. The base of the triangle, the red segment in the image below, will have a length of 20, and the height from B will be 10. Therefore, the area of the triangle will be \(\frac{1}{2}*20*10 = 100\). Sufficient.




Answer: D