chapter 11 - transformations

7/25/2019 Chapter 11 - Transformations

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Chapter 11: Transformations

Paper 1

This test paper contains 20 questions. Answer ALL the questions.The diagrams accompanying the questions are not drawn to scale unless mentioned.

You are allowed to use a scientific calculator that cannot be programmed.

1 Diagram 1 shows pointRon a artesian plane.

DIAGRAM 1

!ind the image of pointRunder a translation

2"

.

A #$% 0& C #"% '2&B #$% ' (& D #"% ' (&

2 )n Diagram 2%PQis the image ofPQ.

DIAGRAM 2

!ind the translation which transformsPQtoPQ.

A

"(

C

(

"

1


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B

"

(D

"

(

3 *hich of the following is falseabout a translation+

A A transformation which in,ol,es only straight line mo,ement.

B An ob-ect and its image are congruent.C ,ery point in an ob-ect mo,es in the same direction through an equal

distance.

D The orientation of an ob-ect and its image are different.

4 A translation transforms a pointA#'/% "& to its imageA#$%'1&. The translation is

A

/10

C

/(

B

0

(D

/

(

5 )nDiagram $% trianglesA, B, C, D andPare drawn on a artesian plane.

DIAGRAM 3

Among the triangles A, B, C and D% which is the image of P under the translation

0

+

2


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6 Diagram ( shows pointPon a artesian plane.

DIAGRAM 4

tate the coordinates of the image ofP( under a reflection in thexa3is.A #(% 2& C #(% '2&

B #'(% '2& D #'(% 0&

)n Diagram %His the image ofHunder a certain reflection.

DIAGRAM 5

*hich of the following is the a3is of the reflection+

A VW C xa3is

B PQ D ya3is

! *hich of the following point "oes notchange its position under a reflection+

A The origin

B 4oints on thexa3is

C 4oints on theya3is

D 4oints on the a3is of reflection

3


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# Diagram " is drawn on a grid.

DIAGRAM 6

Among the triangles A% B% Cand D% which is the image ofPunder a reflection in thea3is VW+

1$ )n Diagram /%Pis the image ofPunder a reflection in the a3is VW.

DIAGRAM

!ind the ob-ectP.

A #2% $& C #2% '$&

B #'2% $& D #'$% 2&

4


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11 )n Diagram 5% the point Pundergoes a cloc6wise rotation about the origin through

an angle of 708.

DIAGRAM !

!ind the image ofP.

A #'2% $& C #2% $&

B #$% '2& D #'$% 2&

12 )n Diagram 7% the linesEF% GF%IJ%KL andVWare on artesian plane.

DIAGRAM #

*hich line is the image of VWunder an anticloc6wise rotation about the originthrough an angle of 708+

A EF C HG

B IJ D KL

5


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13 )n Diagram 10% triangleA9 is the image of triangleAunder a rotation through 708.

DIAGRAM 1$

!ind the centre of rotation.

A #$% 1& C #0% 1&

B #'2% 1& D #1% 1&

14 Diagram 11 shows pointsPand Qon a artesian plane.

DIAGRAM 11

!ind the image of Qunder an anticloc6wise rotation aboutPthrough an angle of 708.

A #$% '1& C #2% 0&

B #'1% '$& D #0% 0&

6


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15 Diagram 12 shows two triangles.

DIAGRAM 12

PQis the image ofPQunder

A a translation

B a reflection in the a3isPP

C a rotation in a cloc6wise direction about the centreRthrough 708

D a rotation through 1508 about the centreR

16 )n Diagram 1$% the triangles are drawn on a grid.

DIAGRAM 13

TrianglePcan be transformed to trianglePby

A a translation C a reflection

B a rotation D an enlargement

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1 Diagram 1( is drawn on a grid.

DIAGRAM 14

TriangleRcan be transformed to triangleRby

A a reflection only

B a rotation only

C a translation or a reflection

D a reflection or a rotation

1! )n Diagram 1%ABCDis a square measuring 5 units by 5 units while AFEDis a

rectangle measuring 5 units by ( units.

DIAGRAM 15

:ectangleAFED can be transformed into rectangleFBCEby

A a translation only

B a rotation or a reflection

C a translation or a rotation

D a translation or a rotation or a reflection

8


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1# )n Diagram 1"% the triangles are drawn on a grid.

DIAGRAM 16

*hich triangles are congruent with triangleP+

A ) only C ) and )) only

B )) only D )% )) and ); only

2$ *hich of the following is nottrue+

A )sometry refers to a transformation where an ob-ect and its image are

congruent.

B !igures ha,ing the same si


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Paper 2

This test paper contains 10 questions. Answer ALL the questions.

The diagrams accompanying the questions are not drawn to scale unless mentioned.

You are not allowed to use a calculator.

1 The image of pointP#2% '& undergoing a translation

"

/is =========.

2 Diagram 1 is drawn on a grid.

DIAGRAM 1

The translation is represented by =============.

3 )n Diagram 2% the triangles are drawn on a grid.

DIAGRAM 2

The translation which transforms trianglePto triangle Qis =======.

4 A reflection in the xa3is will transform point P #'$% '2& to point Q. tate thecoordinates of point Q.

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5 )n Diagram $% pointAis reflected in the linePQ.

DIAGRAM 3

tate the coordinates of the image ofA.

6 )n Diagram (% trianglePOQand triangleFOEare on a artesian plane.

O

DIAGRAM 4

tate the transformation which transforms trianglePOQto triangleFOE.

)n Diagram % the pointPis transformed toPunder a cloc6wise rotation about the

origin through 708.

O

DIAGRAM 5

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tate the coordinates ofP.

! )n Diagram "% the point Qis on a artesian plane.

DIAGRAM 6

tate the coordinates of the image of Qunder an anticloc6wise rotation about the

centre #' 1% 1& through an angle of 1508.

# )n Diagram /% the pointsAtoJare on a artesian plane.

DIAGRAM

Among the pointsAtoJ% which is notan image ofPunder a rotation about the origin+

1$ )n Diagram 5% the triangles are drawn on a grid.

$ cm P

.7 cm

(.$ cm

Q

DIAGRAM !

12


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>i,en that trianglesPand Qare congruent% find the perimeter ofP.

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chapter 11 - transformations

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