Understanding the Cartesian Plane

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Understanding the Cartesian Plane — Free MYP3 Mathematics Practice Questions

1QuestionPlotting Points in All Four QuadrantsConcept Practice

3 marks~5 minCriterion A

Three vertices of a rectangle are plotted on a Cartesian plane:

A(-2,\ 3)

B(4,\ 3)

, and

C(4,\ -1)

Calculate the coordinates of the fourth vertex,

D

. [1]

Identify the quadrant in which each of the four vertices

A

B

C

, and

D

is located. [1]

Explain how the signs of the

x

- and

y

-coordinates of a point determine which quadrant it lies in, using two of the four vertices as examples. [1]

Solutions

2QuestionDescribing Positions Using CoordinatesAssessment Practice

4 marks~6 minCriterion D

A city planner places three bus stops on a coordinate map at:

A(2, 3)

\quad

B(5, 3)

\quad

C(5, 7)

Each unit represents 100 metres. The actual road distances are:

A

B

= 350 m, and

B

C

= 500 m.

Calculate the straight-line distance, in metres, from

A

B

and from

B

C

. [2]

Explain why the coordinate model underestimates the actual walking distances, and suggest one way to improve the model. [2]

Solutions

3QuestionUnderstanding Axes Symmetry in CoordinatesAssessment Practice

5 marks~8 minCriterion C

A student claims that quadrilateral

ABCD

, with vertices

A(2,3)

B(4,5)

C(6,3)

, and

D(4,1)

, is symmetric across the

y

-axis.

Apply the transformation rule

(x, y) \rightarrow (-x, y)

to calculate the reflected coordinates of

A

B

C

, and

D

. [2]

Explain why the reflected quadrilateral is or is not in the same position as the original. [1]

Justify whether the student's claim is true or false, using your results from part (a). [2]

Solutions

4QuestionUnderstanding Axes Symmetry in CoordinatesAssessment Practice

5 marks~8 minCriterion B

Four points are plotted on the Cartesian plane:

P(3,\ 2)

\quad Q(-1,\ 4)

\quad R(-3,\ -2)

\quad S(1,\ -4)

Calculate the coordinates of the reflections of

P

Q

R

, and

S

across the

x

-axis, the

y

-axis, and the origin. [3]

Explain why reflecting any point

(a,\ b)

across the

x

-axis gives the image

(a,\ -b)

, referring to distance from the

x

-axis in your answer. [1]

Using your results from part (a), justify whether the reflection of a point across the

y

-axis and then across the

x

-axis gives the same image as a single reflection across the origin. [1]

Solutions

Questions 5-61

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