AMC 8 Daily Practice Round 11

Complete problem set with solutions and individual problem pages

Problem 14 Medium

As shown in the figure, the coordinates of points A and B are (1, 2) and (3, 0), respectively. The triangle \triangle OAB is translated along the positive x-axis so that point B moves to point E, forming the triangle \triangle DCE. If OE = 4, what are the coordinates of point C?

  • A.

    \left(2,2\right)

  • B.

    \left(3,2\right)

  • C.

    \left(1,3\right)

  • D.

    \left(1,4\right)

  • E.

    (3,1)

Answer:A

By analyzing the problem, we know that point B(3, 0) satisfies OB = 3. Since OE = 4, we calculate BE = OE - OB = 1. Therefore, \triangle OAB is translated 1 unit to the right along the x-axis to form \triangle DCE. Point A is also shifted 1 unit to the right, resulting in point C having coordinates (1+1, 2) = (2, 2). Thus, the correct answer is \textbf{A}.

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