Enlargements revision pack

Transcription

1 When looking at enlargements you need a scale factor and a centre of enlargement. e clear which is the original shape (object) and which is the enlarged shape (image) don t confuse the two! Finding a scale factor and centre of enlargement oints to consider: For it to be an enlargement, the shapes must be similar. Find the scale factor by comparing the lengths of similar sides. Find the centre of enlargement by drawing straight lines through similar points and seeing where they cross. ry with at least three different lengths and points to check for errors. Example 1 Shape has been enlarged to give shape. Find the scale factor and centre of enlargement. You should notice: he base and height of shape are twice that of shape. he lines through three sets of similar points cross at (0, 2) nswer: has been enlarged by scale factor 2, centre of enlargement (0, 2) Example 2 Shape has been enlarged to give shape. Find the scale factor and centre of enlargement. You should notice: he base and height of shape are three times that of shape he lines through three sets of similar points cross at (4, 6). his is an example where the centre of enlargement lies inside the shapes. nswer: has been enlarged by scale factor 3, centre of enlargement (4, 6) age 1 of 6

2 ractice: Finding a scale factor and centre of enlargement In each diagram, shape has been enlarged to give shape. Find the scale factor and centre of enlargement for each. a) scale factor: b) scale factor: c) scale factor: d) scale factor: e) scale factor: f) scale factor: age 2 of 6

3 When looking at enlargements you need a scale factor and a centre of enlargement. e clear which is the original shape (object) and which is the enlarged shape (image) don t confuse the two! Enlarging a shape by a given scale factor and centre of enlargement oints to consider: Diagrams must always be drawn with a sharp pencil, and straight lines must be drawn with a ruler. Leave your construction lines visible as part of your answer. Some questions will tell you how to label your image: o Enlarge shape and label the image. If you are not told how to label your image, use the same letter(s) as the object followed by an apostrophe: o the image of is labelled o the image of triangle is labelled Example Enlarge shape by scale factor 2, centre of enlargement (0, 0). You should: 1. lot the centre of enlargement. 2. Draw a line from the centre of enlargement to one corner of the shape. Extend this line beyond the shape until it is twice as long (as we are using scale factor 2). 3. Repeat for two other corners on the shape. 4. Join up the corners to create the image and label it as. 5. heck your work by comparing the lengths of the sides. Is the height of the new shape twice the height of the original? re the angles unchanged? nswer age 3 of 6

4 ractice: Enlarging a shape by a given scale factor and centre of enlargement a) Use centre of enlargement (0, 0) and scale factor 2 to enlarge square D. b) Enlarge shape using centre of enlargement (0, 5) and scale factor 2. D c) Use centre of enlargement (0, 2) to enlarge the letter M by a scale factor of 3. Label the image as. d) Use centre of enlargement (2, 0) and scale factor 3 to enlarge arrow, to give image R. e) Use centre of enlargement (0, 4) and scale factor 3 to enlarge triangle. f) Use centre of enlargement (2, 2) to enlarge hexagon by a scale factor ½ age 4 of 6

5 nswers Finding a scale factor and centre of enlargement a) scale factor: 3 b) scale factor: 2 (0, 1) (1, 0) c) scale factor: 3 d) scale factor: 2 (0, 5) (4, 2) e) scale factor: 2 f) scale factor: ½ (0, 10) (0, 0) Enlarging a shape by a given scale factor and centre of enlargement a) b) D D c) d) R e) f) age 5 of 6

6 eaching notes his resource addresses two enlargement techniques: finding a scale factor and centre of enlargement enlarging a shape by a given scale factor and centre of enlargement. It contains two sets of student facing notes and example questions with accompanying practice sheets, and is ideal for: a revision guide for independent revision. Students may wish to highlight and annotate the notes and examples. cover lessons. You could choose whether to provide the notes for the students or as a guide for the cover teacher. separate resource sheets. he practice questions are given on separate sheets so could be used without the notes age 6 of 6