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Rectangle ABCD is drawn in the xy-plane such that side AB is parallel to the x-axis and the side AD is parallel to the y-axis. What are the coordinates of point D?
(1) The coordinates of point A are (2, 3)
(2) The coordinates of point C are (4, 8)
  • a)
    Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
  • b)
    Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
  • c)
    BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
  • d)
    EACH statement ALONE is sufficient to answer the question asked.
  • e)
    Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Rectangle ABCD is drawn in the xy-plane such that side AB is parallel ...
Steps 1 & 2: Understand Question and Draw Inferences
Given: Rectangle ABCD in the xy-plane
  • Since AB is parallel to the x-axis,
    • Points A and B will have the same y-coordinates
    • Since side CD of the rectangle will be parallel to side AB, points C and D too will have the same y-coordinates
  • Since AD is parallel to the y-axis,
    • Points A and D will have the same x-coordinates
    • Since side BC of the rectangle will be parallel to side AD, points B and C too will have the same x-coordinates
 
To find: Coordinates of point D
Step 3: Analyze Statement 1 independently
Statement 1 says that ‘The coordinates of point A are (2, 3)’
  • This means, the x-coordinate of point D is 2
  • However, since we do not know the y-coordinate of point D, Statement 1 alone is not sufficient
 
Step 4: Analyze Statement 2 independently
Statement 2 says that ‘The coordinates of point C are (4, 8)’
  • This means, the y-coordinate of point D is 8
  • However, since we do not know the x-coordinate of point D, Statement 2 alone is not sufficient
 
Step 5: Analyze Both Statements Together (if needed)
  • From Statement 1, the x- coordinate of point D is 2
  • From Statement 2, the y-coordinate of point D is 8
  • So, the coordinates of point D are (2,8)
Thus, by combining the 2 statements, we do get a unique answer
Answer: Option C
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Rectangle ABCD is drawn in the xy-plane such that side AB is parallel to the x-axis and the side AD is parallel to the y-axis. What are the coordinates of point D?(1) The coordinates of point A are (2, 3)(2) The coordinates of point C are (4, 8)a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.c)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.d)EACH statement ALONE is sufficient to answer the question asked.e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.Correct answer is option 'C'. Can you explain this answer?
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