ROTATIONDescribe how the triangle A was transformed tomake triangle BA BTriangle A was rotated 90 clockwise at thecentre of rotation P(x, y)P(x, y)
ROTATIONDescribe how the arrow A was transformed to makearrow BDescribe the transformation.Arrow A was rotated 180 clockwise/anticlockwise at the centre of rotation P(x, y)ABP (x, y)
REFLECTIONA REFLECTION IS FLIPPED OVER A LINE.A reflection is a transformation that flipsa figure across a line.
REFLECTIONThe line that a shape is flipped over is called aline of reflection or axis of reflection.A REFLECTION IS FLIPPED OVER A LINE.Line/ axis ofreflectionNotice, the shapes are exactly the samedistance from the line of reflection on bothsides.The line of reflection can be on the shapeor it can be outside the shape.
CONCLUSIONWe just discussed three types of transformations.See if you can match the action with theappropriate transformation.FLIPSLIDETURNREFLECTIONTRANSLATIONROTATION
Translation, Rotation, and Reflection allchange the position of a shape, while thesize remains the same.The fourth transformation that we aregoing to discuss is calledENLARGEMENT (dilation).
TRANSFORMATIONSCHANGE THE POSTIONOF A SHAPECHANGE THE SIZE OF ASHAPETRANSLATION ROTATION REFLECTIONChange inlocationTurn around apointFlip over alineENLARGEMENTChange size ofa shapeTranslation ( )- distance- directionxy- centre P(x, y)- direction- angle spins- Line/axis ofreflection- distance- backward- centre P(x, y)- scale factor, k
Enlargement changes the size of theshape without changing the shape.ENLARGEMENTWhen you enlarge a photograph or use acopy machine to reduce a map, you aremaking enlargement with -1< k <1.
Enlarge means to make a shape bigger.ENLARGEMENTReduce means to make a shape smaller.The scale factor tells you how muchsomething is enlarged or reduced.
SimilaritySimilar figures have the same shape:-All the corresponding angles are equal or-All the corresponding sides are the same ratioABA’B’D D’CC’BB’A’A=DAD’A’CDC’D’BCB’C’==
A scale factor describes how much a figure isenlarged or reduced. A scale factor can beexpressed as a decimal, fraction, or percent. A 10%increase is a scale factor of 1.1, and a 10%decrease is a scale factor of 0.9.
Scale factor of enlargement, kA’C’CB’BAk = A’B’AB= 74= 1.75k = length of imagelength of object
A scale factor (k) between 0 and 1 reduces afigure. A scale factor greater than 1 enlarges it.-1<k<1 image is smaller than the object-1>k>1 image is larger than the objectk=1 or k=-1 image is equal to the object-k image and object are in opposite directionHelpful Hint
Tell whether each transformation is aenlargement.The transformationis a enlargement.The transformationis not a enlargement.The figure is distorted.A. B.Example: Identifying Enlargement
Every enlargement has a fixed point that isthe centre of enlargement. To find thecentre of enlargement, draw a line thatconnects each pair of correspondingvertices. The lines intersect at one point.This point is the centre of enlargement.
Enlarge the figure by a scale factor of 1.5 withP as the center of enlargement.Multiply each side by 1.5.Example: Enlarging a Figure
Enlarge the figure by a scale factor of 0.5 withG as the center of enlargement.GF H2 cm 2 cm2 cmMultiply each side by 0.5.GF H2 cm2 cm2 cmF’ H’1 cm1 cm1 cmTry This
Determine the centre of enlargementP(-2, 3)A’C’CB’BAxy-2 86422640-2Centre ofenlargement, P(-2, 3)
Enlarge the figure by a scale factor of 2 withorigin is the centre of enlargement.242 4 6 8 1006810BCAImage Of Enlargement
242 4 6 8 1006810B’C’A’BCAImage Of EnlargementGiven k = 2,Origin is the centre ofenlargementA’B’ = AB x k= 2 x 2= 4 unit
Enlarge the figure by a scale factor of 0.5 withorigin is the centre of enlargement.242 4 6 8 1006810BCAImage Of Enlargement
242 4 6 8 1006810BCAB’C’A’Image Of EnlargementA’B’ = AB x k= 4 x 0.5= 2 unitGiven k = 0.5,Origin is the centre ofenlargement
Area Of ImageIf k is the scale of an enlargement,Area of ImageArea of Objectk2 =
Skill PracticePoster B is an enlargement of A with scale factor 5. If the area ofposter A is 600cm2,.find the area of poster B.Area of ImageArea of Objectk2 =52 = Area of Poster B600= 600 x 25Area of Poster B= 15,000 cm2
Skill PracticeIn the figure, the bigger circle is the Imageof the smaller circle under an enlargementcentre O and scale factor 2, Given that thearea of the smaller circle is 15 cm2,calculate the area of the shaded regionArea of ImageArea of Objectk2 =22 = Area of Image15= 15 x 4Area of image= 60 cm2oArea of shaded region = 60 - 15= 45 cm2
Look at the pictures belowENLARGEMENTEnlarge the image with a scalefactor of 75%Enlarge the image with a scalefactor of 150%
See if you can identify the transformation thatcreated the new shapesTRANSLATION
See if you can identify the transformation thatcreated the new shapesREFLECTIONWhere is the lineof reflection?
See if you can identify the transformation thatcreated the new shapesROTATION
See if you can identify the transformation thatcreated the new shapesENLARGEMENT