Geometrical Transformations

You're viewing free preview questions — 4 questions previewing here — subscribe to unlock 164 more, plus the Full Question Bank, Mock Papers & Worksheets.Upgrade

Geometrical Transformations — Free MYP4 Mathematics (Extended) Practice Questions

1QuestionDescribing and Performing TranslationsConcept Practice

2 marks~3 minCriterion A

A city planner is mapping a park renovation. On the coordinate grid, a triangular flower bed

ABC

has been repositioned to a new location

A'B'C'

using a single translation.

Point

A

has coordinates

(1, 2)

and its image

A'

has coordinates

(5, -1)

Determine the translation vector that maps triangle

ABC

to triangle

A'B'C'

. Give your answer in the form

\dbinom{x}{y}

. [1]

The planner states: "The flower bed has moved further east than it has moved south." Justify whether the planner's statement is correct. [1]

Solutions

2QuestionReflections in Lines x-axis y-axis y=x y=-xAssessment Practice

5 marks~8 minCriterion C

A graphic designer uses coordinate geometry to plan a logo. Triangle

PQR

is reflected in the line

y = x

to produce triangle

P'Q'R'

, with

P'(3, 1)

Q'(5, 2)

, and

R'(2, 4)

Find the coordinates of

P

and

R

. [1]

Reflect segment

PR

in the line

y = -x

. Write the coordinates of the image endpoints

P''

and

R''

, and find the equation of segment

P''R''

. [3]

The designer claims that point

S(1, 3)

lies on segment

P''R''

and therefore falls within the logo boundary. Justify whether this claim should be accepted before the designer finalises the logo. [1]

Solutions

3QuestionEnlargement with Positive and Negative Scale FactorsAssessment Practice

6 marks~9 minCriterion D

An architect is designing a mirrored facade for a building. A decorative triangular panel has vertices at

A(2,\ 1)

B(5,\ 1)

, and

C(3,\ 4)

on a blueprint (units in metres). The triangle is enlarged by a scale factor of

-0.5

with centre of enlargement at the origin.

The construction team marks points with a tolerance of

\pm 0.05\ \text{m}

in each coordinate, independently.

Determine the coordinates of the image vertices

A'

B'

, and

C'

. [2]

Calculate the maximum possible area of the constructed triangle, and hence find the maximum area error compared to the theoretical image. [3]

Advise the architect whether this enlargement transformation is appropriate for large-scale construction, addressing: the effect of tolerances on accuracy; one practical limitation of using a negative scale factor on site; and one broader limitation of applying geometric transformations directly to construction. [1]

Solutions

4QuestionRotations About a Point and AngleAssessment Practice

8 marks~12 minCriterion B

A video-game developer is programming a camera rotation feature. A triangular obstacle has vertices at

A(2,3)

B(5,1)

, and

C(4,6)

. After a

90°

clockwise rotation about the origin, the image vertices are

A'(3,-2)

B'(1,-5)

, and

C'(6,-4)

Describe the relationship between the coordinates of each original vertex and its image. [2]

Deduce a general rule for the image of any point

(x, y)

under a

90°

clockwise rotation about the origin. [2]

A sensor is located at

D(-3, 4)

. Apply your rule to find the image

D'

. [2]

The developer claims that rotating the sensor's position does not change its distance from the camera (origin). Justify whether this claim is consistent with your result for

D

and

D'

. [2]

Solutions

Questions 5-168

Unlock these questions with Premium

That's every free question here — 4 of 168.

+164 more questions, plus Mock Papers & Worksheets, are waiting in Premium.

Upgrade