Plotting Points in the Plane MCQs

Q1. Three corners of a rectangular table are at (8, 9), (11, 9) and (11, 7). Where is the fourth foot?

• A.(8, 7)
• B.(11, 9)
• C.(8, 9)
• D.(8, 11)

Answer: A. (8, 7)

From the stem we have: 8; 9; 11; 9; 11. To find: the unknown asked in the stem. Formula: recall the relevant relation from this chapter (math, chapter 'Coordinate Geometry') that ties the given data to the unknown. Why this is the right approach - fourth corner shares x with first (8) and y with third (7). Therefore the answer is A) (8, 7). Ruling out the other options: option B) '(11, 9)' is incorrect: That is one of the given corners; option C) '(8, 9)' is wrong because That is one of the given corners; option D) '(8, 11)' misses the point - The fourth corner is opposite to (11, 9); share x = 8, y = 7.

Q2. Three corners of a rectangular table are at (2, 3), (5, 3) and (5, 1). Where is the fourth foot?

• A.(2, 1)
• B.(5, 3)
• C.(2, 3)
• D.(2, 5)

Answer: A. (2, 1)

From the stem we have: 2; 3; 5; 3; 5. What we must find: the unknown asked in the stem. The relation that links these is: recall the relevant relation from this chapter (math, chapter 'Coordinate Geometry') that ties the given data to the unknown. Reasoning behind the choice of formula - fourth corner shares x with first (2) and y with third (1). Therefore the answer is A) (2, 1). The other choices: option B) '(5, 3)' fails since That is one of the given corners; option C) '(2, 3)' is incorrect: That is one of the given corners; option D) '(2, 5)' doesn't hold - The fourth corner is opposite to (5, 3); share x = 2, y = 1.

Q3. Three corners of a rectangular table are at (-1, 4), (3, 4) and (3, 2). Where is the fourth foot?

• A.(-1, 2)
• B.(3, 4)
• C.(-1, 4)
• D.(-1, 6)

Answer: A. (-1, 2)

Data from the problem: -1; 4; 3; 4; 3. To find: the unknown asked in the stem. Relation we use: recall the relevant relation from this chapter (math, chapter 'Coordinate Geometry') that ties the given data to the unknown. Why this is the right approach - fourth corner shares x with first (-1) and y with third (2). Putting it together the answer is A) (-1, 2). Where the distractors go off: option B) '(3, 4)' is incorrect: That is one of the given corners; option C) '(-1, 4)' fails since That is one of the given corners; option D) '(-1, 6)' doesn't hold - The fourth corner is opposite to (3, 4); share x = -1, y = 2.