Plotting Points and Interpreting Coordinates
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Plotting Points and Interpreting Coordinates — Free MYP3 Mathematics Practice Questions

1QuestionFinding Missing Coordinates in ShapesConcept Practice
2 marks~3 minCriterion D
A city planner is designing a rectangular plaza with benches at each corner. On a coordinate grid where 1 unit = 1 metre, three corners are placed at A(2,1)A(2, 1), B(2,6)B(2, 6), and C(7,1)C(7, 1).

Explain one reason why using a coordinate system to locate the missing corner is more accurate than estimating its position during construction. [2]
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Solutions

2QuestionFinding Missing Coordinates in ShapesAssessment Practice
4 marks~6 minCriterion B
Three vertices of a rectangle are plotted on a coordinate grid: A(1,2)A(1,2), B(5,2)B(5,2), and C(5,6)C(5,6).
a
Plot points AA, BB, and CC on the grid. Calculate the coordinates of the fourth vertex, DD. [1]
b
A second rectangle has vertices P(−3,1)P(-3,1), Q(4,1)Q(4,1), and R(4,5)R(4,5). Explain how you know where the fourth vertex SS must lie, and state its coordinates. [1]
c
A third rectangle has three known vertices X(2,3)X(2,3), Y(7,3)Y(7,3), and Z(7,8)Z(7,8). Analyse the coordinates of all five known vertices from parts (a) and (b) to write a general rule for finding the missing vertex of any axis-aligned rectangle. Apply your rule to find the missing vertex WW. [2]
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Solutions

3QuestionFinding Missing Coordinates in ShapesConcept Practice
5 marks~8 minCriterion A
Rectangle ABCDABCD has three known vertices: A(1,2)A(1, 2), B(1,5)B(1, 5), and C(6,5)C(6, 5). The diagonals of a rectangle bisect each other.
a
Calculate the midpoint of diagonal ACAC. [2]
b
Calculate the coordinates of vertex DD, given that the midpoint of diagonal BDBD equals the midpoint of diagonal ACAC. [2]
c
A student claims that DD must lie on the line x=1x = 1 because AA has xx-coordinate 11. Explain why this claim is incorrect. [1]
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Solutions

4QuestionUnderstanding Midpoint Between Two PointsConcept Practice
5 marks~8 minCriterion C
A student claims that C(4, 5)C(4,\ 5) is the midpoint of the line segment joining A(1, 2)A(1,\ 2) and B(7, 8)B(7,\ 8).
a
Apply the midpoint formula to find the midpoint MM of segment ABAB. [2]
b
Compare your answer to point CC and explain whether the student's claim is correct. [2]
c
A second student says: "Any point with an xx-coordinate of 4 must be the midpoint of ABAB." Justify whether this statement is correct or incorrect. [1]
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Solutions

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