Manhatten Prep Geometry: Why does this approach not work?

GRE Quant Problem Solving
1

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

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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?

2

Formula for distance between 2 points is Root((x2-x1)^2 + (y2-y1)^2), You got length of AB correct as 5 so now length of BC should be 10. This means than 100 = (difference(x2,x1)^2 + difference(y2,y1)^2) based on formula

You have one set of x,y as 3,4 and you can use other sets from options to eliminate others based above highlighted equation

For C only, above equation doesn’t holds true as ((10-3)^2+(11-4)^2) = (49+49) which is not equal to 100. Not sure about technique but this is how I figured it out

3

The technique you described is already given in the book and I fully understand it. I am just trying to figure out if any of the assumptions I made when solving the problem by my method are wrong (so that I don’t make the same mistake when solving other problems by using the same assumptions).