Geometry IV Transformation Geometry and Enlargements Solutions Practice

Geometry IV: Transformation Geometry and Enlargements Solutions: Practice Questions 13. 3 CHAPTER 13

Practice Questions 13. 3 13 1. (i) Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. Scale factor 2 Steps: 1. Measure the distance between O and each vertex. 2. Multiply this distance by 2. 3. Draw a line from O through each vertex whose length is equal to the length calculated in Step 2. 4. Join these points to form the image.

Practice Questions 13. 3 13 1. (ii) Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. Scale factor 4 Steps: 1. Measure the distance between O and each vertex. 2. Multiply this distance by 4. 3. Draw a line from O through each vertex whose length is equal to the length calculated in Step 2. 4. Join these points to form the image.

Practice Questions 13. 3 13 1. (iii) Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. Scale factor 3 Steps: 1. Measure the distance between O and each vertex 2. Multiply by 3. Draw a line from O through each vertex whose length is equal to the length calculated in Step 2. 4. Join these points to form the image.

Practice Questions 13. 3 13 1. (iv) Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. Scale factor 4 Steps: 1. Measure the distance between O and each vertex 2. Multiply by 4. 3. Draw a line from O through each vertex whose length is equal to the length calculated in Step 2. 4. Join these points to form the image.

Practice Questions 13. 3 13 1. (v) Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. Scale factor 2 Steps: 1. Measure the distance between O and each vertex 2. Multiply by 2. 3. Draw a line from O through each vertex whose length is equal to the length calculated in Step 2. 4. Join these points to form the image.

Practice Questions 13. 3 13 1. (vi) Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. Scale factor 3 Steps: 1. Measure the distance between O and each vertex 2. Multiply by 3. Draw a line from O through each vertex whose length is equal to the length calculated in Step 2. 4. Join these points to form the image.

13 2. (i) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor Steps: 1. 2. Measure the distance between O and each vertex this distance. 3. Draw a line of this length from O through the vertex. 4. Repeat for each vertex. 5. Join to from image.

13 2. (i) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor

13 2. (ii) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor Steps: 1. Measure the distance between O and each vertex 2. Divide the distance by 3. Draw a line of this length from O through the vertex. 4. Repeat for each vertex. 5. Join to from image.

13 2. (ii) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor

13 2. (iii) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor Steps: 1. Measure the distance between O and each vertex 2. Divide the distance by 4. 3. Draw a line of this length from O through the vertex. 4. Repeat for each vertex. 5. Join to from image.

13 2. (iii) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor

13 2. (iv) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor Steps: 1. Measure the distance between O and each vertex 2. Multiply the distance by 3. Draw a line of this length from O through the vertex. 4. Repeat for each vertex. 5. Join to from image. .

13 2. (iv) Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre of enlargement shown and scale factor given. Scale factor

13 3. Practice Questions 13. 3 Copy the following shape on to graph paper and complete the enlargement with centre of enlargement at the origin (0, 0) and given scale factor. (i) Scale factor 2 Steps: 1. Measure the distance between O and each vertex 2. Multiply the distance by 2. 3. Draw a line of this length from O through the vertex. 4. Repeat for each vertex. 5. Join to from image.

13 3. Practice Questions 13. 3 Copy the following shape on to graph paper and complete the enlargement with centre of enlargement at the origin (0, 0) and given scale factor. Scale factor 2

13 3. Practice Questions 13. 3 Copy the following shape on to graph paper and complete the enlargement with centre of enlargement at the origin (0, 0) and given scale factor. (ii) Scale factor Steps: 1. Measure the distance between O and each vertex 2. Multiply the distance by 3. Draw a line of this length from O through the vertex. 4. Repeat for each vertex. 5. Join to from image. .

13 3. Practice Questions 13. 3 Copy the following shape on to graph paper and complete the enlargement with centre of enlargement at the origin (0, 0) and given scale factor. Scale factor

13 3. Practice Questions 13. 3 Copy the following shape on to graph paper and complete the enlargement with centre of enlargement at the origin (0, 0) and given scale factor. (iii) Comment on the size difference between the object and its image under each of the enlargements above. Scale factor 2: Scale factor The lengths of the sides of the image are all twice the lengths of sides of the object when the scale factor is 2. : The lengths of the sides of the image are all one third the lengths of the sides of the object when the scale factor is.

Practice Questions 13. 3 13 4. Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (i) Steps: 1. Draw a line through each point on the object and its corresponding point on the image. 2. Extend these lines until they meet. 3. Mark this point as the centre of enlargement.

13 4. Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (i) Centre of enlargement = (0, 1)

Practice Questions 13. 3 13 4. Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (ii) Steps: 1. Draw a line through each point on the object and its corresponding point on the image. 2. Extend these lines until they meet. 3. Mark this point as the centre of enlargement.

13 4. Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (ii) Centre of enlargement = (1, 0)

Practice Questions 13. 3 13 4. Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (iii) Steps: 1. Draw a line through each point on the object and its corresponding point on the image. 2. Extend these lines until they meet. 3. Mark this point as the centre of enlargement.

13 4. Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (iii) Centre of enlargement = (0, 5)

Practice Questions 13. 3 13 4. Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (iv) Steps: 1. Draw a line through each point on the object and its corresponding point on the image. 2. Extend these lines until they meet. 3. Mark this point as the centre of enlargement.

13 4. Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (iv) Centre of enlargement = (4, 2)

Practice Questions 13. 3 13 4. Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (v) Steps: 1. Draw a line through each point on the object and its corresponding point on the image. 2. Extend these lines until they meet. 3. Mark this point as the centre of enlargement.

13 4. Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (v) Centre of enlargement = (0, 10)

Practice Questions 13. 3 13 4. Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (vi) Steps: 1. Draw a line through each point on the object and its corresponding point on the image. 2. Extend these lines until they meet. 3. Mark this point as the centre of enlargement.

13 4. Practice Questions 13. 3 Copy the following shapes on to graph paper and complete the enlargement with centre O and the given scale factor. (vi) Centre of enlargement = (0, 0)

13 5. (i) Practice Questions 13. 3 Use the grid to find the scale factor of enlargement from A to B in each of the following:

13 5. (ii) Practice Questions 13. 3 Use the grid to find the scale factor of enlargement from A to B in each of the following:

13 5. (iii) Practice Questions 13. 3 Use the grid to find the scale factor of enlargement from A to B in each of the following:

13 5. (iv) Practice Questions 13. 3 Use the grid to find the scale factor of enlargement from A to B in each of the following:

13 5. (v) Practice Questions 13. 3 Use the grid to find the scale factor of enlargement from A to B in each of the following:

13 6. Practice Questions 13. 3 A photograph is 8 cm long. It is enlarged by a scale factor of three. How long will the enlarged photo be? Object length = 8 cm Scale factor = 3

13 7. Practice Questions 13. 3 Alex made a scale diagram of the plan for his garden. The garden measures 18 m by 12 m. On the scaled diagram, the longer side measures 8 cm. What is the length of the shorter side in the diagram? Garden length = 18 m 1 m = 100 cm 18 m = 100 � 18 cm 18 m = 1800 cm Diagram length = 8 cm

13 7. Practice Questions 13. 3 Alex made a scale diagram of the plan for his garden. The garden measures 18 m by 12 m. On the scaled diagram, the longer side measures 8 cm. What is the length of the shorter side in the diagram? Scale factor applies to both length and width, so

13 8. (i) Practice Questions 13. 3 Diana is editing a digital photo that is 640 pixels wide and 480 pixels high on her computer screen. Suppose Diana wants to use the photograph on a web page and wants the image to be 32 pixels wide. What scale factor should she use to reduce the image? Object width (photo) = 640 pixels Image width (web page) = 32 pixels

13 8. (ii) Practice Questions 13. 3 Diana is editing a digital photo that is 640 pixels wide and 480 pixels high on her computer screen. She decides to resize the original photo so that it is 600 pixels high. What scale factor did she use? Object height (photo) = 480 pixels Image height (resize) = 600 pixels

13 9. Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. (i) Give the scale factor of enlargement for A to B. Object = A Image = B Object height = 28 cm Image height = 42 cm

13 9. Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. (ii) Give the scale factor of enlargement of the perimeter for A to B. Perimeter of circle = 2 r r = radius Perimeter of semicircle = r

13 9. Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. (ii) Give the scale factor of enlargement of the perimeter for A to B. Perimeter of A = 28 + 42 + 28 + r Perimeter of A = 28 + 42 + 28 + 65· 97 Perimeter of A = 163· 97 cm

13 9. Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. (ii) Give the scale factor of enlargement of the perimeter for A to B. Perimeter of B = 42 + 63 + 42 + r Perimeter of B = 42 + 63 + 42 + 98· 96 Perimeter of B = 245· 96 cm

13 9. Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. (ii) Give the scale factor of enlargement of the perimeter for A to B.

13 9. Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. (iii) Find the area of A, then use the scale factor of enlargement to find the area of B in square centimetres correct to two decimal places. Area of A = Area of rectangle + Area of semicircle Area of rectangle = length � width Area of rectangle = 42 � 28 Area of rectangle = 1176 cm 2

13 9. Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. (iii) Find the area of A, then use the scale factor of enlargement to find the area of B in square centimetres correct to two decimal places. Area of circle = r 2 Area of semicircle = r = 21 Area of semicircle = 692· 72 cm 2 Area of A = 1176 + 692· 72 Area of A = 1, 868· 72 cm 2

13 9. (iii) Practice Questions 13. 3 Two window frames (shown below) are designed by combining a rectangle and a semicircle. Find the area of A, then use the scale factor of enlargement to find the area of B in square centimetres correct to two decimal places. Scale factor = 1· 5 Area of A = 1868· 72 from (i) and (ii) Object

13 10. (i) Practice Questions 13. 3 Theo has a scale model of a car. If the length of the model car is 45 cm, what is the length of the full-sized car? Scale factor = Model car (image) = 45 cm

13 10. (i) Practice Questions 13. 3 Theo has a scale model of a car. If the length of the model car is 45 cm, what is the length of the full-sized car?

13 10. (ii) Practice Questions 13. 3 Theo has a scale model of a car. If the area of the bonnet of the model is 0· 021 m 2, what is the area of the bonnet of the full-sized car? Bonnet area (image) = 0· 021 m 2 Scale factor =

13 10. (ii) Practice Questions 13. 3 Theo has a scale model of a car. If the area of the bonnet of the model is 0· 021 m 2, what is the area of the bonnet of the full-sized car?