Cartesian Plane and Coordinates

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Cartesian Plane and Coordinates — Free MYP5 Mathematics (Extended) Practice Questions

1QuestionInterpreting 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]

Solutions

2QuestionInterpreting Grids and Map CoordinatesAssessment Practice

3 marks~5 minCriterion D

A park map uses a grid where each unit represents 50 metres. Three landmarks are located at the following coordinates:

Fountain:

(3, 2)

Picnic Area:

(7, 6)

Playground:

(3, 9)

Calculate the straight-line distance, in metres, between the Fountain and the Playground. [1]

Calculate the straight-line distance, in metres, between the Fountain and the Picnic Area. [1]

A path connecting all three landmarks must be under 600 metres in total length to qualify for a park accessibility grant. Justify whether this path qualifies for the grant, using your results from (a) and (b). [1]

Solutions

3QuestionIdentifying Coordinates from a GraphAssessment Practice

3 marks~5 minCriterion A

A city planner is designing a straight pedestrian path between two landmarks. Landmark

P

is located at

(2, 5)

and landmark

Q

is at

(8, 1)

on a scaled map, where each unit represents 100 metres.

A water fountain must be installed at the exact midpoint

M

of path

PQ

Calculate the coordinates of midpoint

M

. [1]

Deduce the straight-line distance from

P

M

, giving your answer in metres. [1]

The city planner states: "The fountain is closer to the city centre at

(4, 4)

than either landmark is." Assess whether this statement is correct, supporting your answer with distance calculations. [1]

Solutions

4QuestionReal-Life Uses of Cartesian CoordinatesAssessment Practice

8 marks~12 minCriterion B

A taxi travels along a straight road through a city grid. GPS tracking records the following positions:

Point A	$x = 1$	$y = 3$
Point B	$x = 2$	$y = 5$
Point C	$x = 3$	$y = 7$
Point D	$x = 4$	$y = 9$

Describe the pattern in the

y

-coordinates as

x

increases by 1, and state the constant difference. [2]

Deduce the coordinates of the next two points, E and F, on the same road. [2]

Determine the equation of the road in the form

y = mx + c

. Explain how the constant difference from part (a) determines the value of

m

. [2]

The taxi dispatcher claims the road passes through the point

(10, 21)

. Justify whether this claim is correct, and interpret what your answer means about the taxi's route. [2]

Solutions

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