This problem is from MANHATTAN PREP Guide 3 Geometry Hard Practice Question Set Question 2. I followed the following approach to solve this problem:

• Find the length of AB = 5

• Find the length of BC = 2AB = 2x5 = 10

• Connect the points B and C, and C and A to form a triangle ABC.

• Based on the lengths of 2 sides (AB and BC), estimate the length of AC to be in the range *5 < x < 15*

• Then I calculated the distance from point A (0, 0) to each of the options:

- Option A: 5.3
- Option B: 15
- Option C: 14.86
- Option D: 14.86
- Option E: 13.6

Since only the length from Option B is out of range for the length of AC, I chose option B as the answer. But the guide says that the answer is C. It uses the value of length BC and eliminates all the options that result in the distance of 10. I understand the approach provided in the guide but shouldn’t the approach I used also work? What did I do wrong?

Question:

In the coordinate plane above, point C is not displayed. If the length of line segment BC is twice the length of line segment AB, which of the following could not be the coordinates of point C?