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Cartesian Plane and Coordinates — Free MYP4 Mathematics (Standard) Practice Questions
1QuestionMidpoint and Distance Between Two PointsConcept Practice
2 marks~3 minCriterion A
A city planner is designing a straight pedestrian path between two landmarks. On a coordinate grid where each unit represents 100 metres, landmark is located at and landmark is located at .
A rest shelter must be placed exactly halfway along the path.
Using the midpoint formula
calculate the coordinates of the midpoint of segment , and hence interpret the real-world position of the shelter relative to landmark , in metres, along each axis direction. [2]
A rest shelter must be placed exactly halfway along the path.
Using the midpoint formula
calculate the coordinates of the midpoint of segment , and hence interpret the real-world position of the shelter relative to landmark , in metres, along each axis direction. [2]
Solutions
2QuestionIdentifying Coordinates from a GraphAssessment Practice
4 marks~6 minCriterion D
A city planner records the cumulative length of a new cycle path at three checkpoints:
, ,
where the -axis shows time elapsed (hours) and the -axis shows distance covered (kilometres). The three points are plotted on the provided graph.
, ,
where the -axis shows time elapsed (hours) and the -axis shows distance covered (kilometres). The three points are plotted on the provided graph.
a
Calculate the slope of the line passing through points and . [1]
b
Explain why point lies on the same straight line as and . [1]
c
Interpret what the slope represents in this context, then advise the city planner whether the current construction rate is sufficient to complete the 20 km path within 9 hours, justifying your answer with a calculation. [2]
Solutions
3QuestionReal-Life Uses of Cartesian CoordinatesConcept Practice
2 marks~3 minCriterion B
A taxi starts at the origin of a coordinate grid, where the horizontal axis represents time (minutes) and the vertical axis represents distance (kilometres). The following positions are recorded:
: : : :
Describe the relationship between and using the general ordered-pair notation , and interpret what this relationship means for the taxi's journey. [2]
: : : :
Describe the relationship between and using the general ordered-pair notation , and interpret what this relationship means for the taxi's journey. [2]
Solutions
4QuestionInterpreting Grids and Map CoordinatesConcept Practice
2 marks~3 minCriterion C
A search-and-rescue team uses a topographic map with a 4-figure grid reference system to locate a missing hiker. The map grid divides the terrain into squares, each representing a 1 km × 1 km area on the ground.
Explain how a 4-figure grid reference identifies a position on the map, and describe one limitation of this system for pinpointing the hiker's exact location. [2]
Explain how a 4-figure grid reference identifies a position on the map, and describe one limitation of this system for pinpointing the hiker's exact location. [2]
Solutions
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