Enlargements worksheet | PPT - Free Printable
Educational worksheet: Enlargements worksheet | PPT. Download and print for classroom or home learning activities.
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Step-by-step solution for: Enlargements worksheet | PPT
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Show Answer Key & Explanations
Step-by-step solution for: Enlargements worksheet | PPT
To solve the problem of enlarging each shape from its Centre of Enlargement A by the given scale factor, you must perform a geometric transformation called an "enlargement" or "dilation." This involves scaling the distance of every point on the shape from the centre point A.
Here is the step-by-step method to complete this task for any of the shapes:
1. Identify the Centre and Vertices: Locate the point labeled 'A' (the Centre of Enlargement) and identify all the vertices (corner points) of the shape.
2. Calculate Vectors: For each vertex, calculate the horizontal and vertical distance (vector) from point A to that vertex. You can do this by counting the number of grid squares horizontally and vertically.
3. Apply the Scale Factor: Multiply both the horizontal and vertical distances by the given scale factor.
* For example, if a vertex is 2 squares to the right and 1 square up from A, and the scale factor is 2, the new position will be 4 squares to the right and 2 squares up from A.
* If the scale factor is 1 1/2 (or 1.5), you would multiply the distances by 1.5. For instance, 2 squares right becomes 3 squares right, and 1 square up becomes 1.5 squares up.
4. Plot the New Vertices: From point A, move the new calculated distances (horizontal and vertical) to plot the position of each new, enlarged vertex.
5. Connect the Points: Draw lines connecting the new vertices in the same order as the original shape to form the enlarged image.
Summary of Each Shape's Transformation:
* Shape 1 (Triangle, Scale Factor 2): The triangle will become twice as large. Each vertex will be twice as far from point A as it was originally.
* Shape 2 (Triangle, Scale Factor 4): The triangle will become four times larger. Each vertex will be four times as far from point A.
* Shape 3 (Square, Scale Factor 2): The square will become twice as wide and twice as tall. Its bottom edge will be twice as far from point A.
* Shape 4 (Diamond, Scale Factor 3): The diamond will become three times larger. Each vertex will be three times as far from point A.
* Shape 5 (Hexagon, Scale Factor 3): The hexagon will become three times larger. Its bottom vertex will be three times as far from point A.
* Shape 6 (L-shape, Scale Factor 2): The L-shape will become twice as large in all dimensions. Each corner will be twice as far from point A.
* Shape 7 (T-shape, Scale Factor 4): The T-shape will become four times larger. Each corner will be four times as far from point A.
* Shape 8 (Parallelogram, Scale Factor 1 1/2): The parallelogram will become 1.5 times larger. Each vertex will be 1.5 times as far from point A.
By following this method for each of the eight shapes, you will have successfully completed the task.
Here is the step-by-step method to complete this task for any of the shapes:
1. Identify the Centre and Vertices: Locate the point labeled 'A' (the Centre of Enlargement) and identify all the vertices (corner points) of the shape.
2. Calculate Vectors: For each vertex, calculate the horizontal and vertical distance (vector) from point A to that vertex. You can do this by counting the number of grid squares horizontally and vertically.
3. Apply the Scale Factor: Multiply both the horizontal and vertical distances by the given scale factor.
* For example, if a vertex is 2 squares to the right and 1 square up from A, and the scale factor is 2, the new position will be 4 squares to the right and 2 squares up from A.
* If the scale factor is 1 1/2 (or 1.5), you would multiply the distances by 1.5. For instance, 2 squares right becomes 3 squares right, and 1 square up becomes 1.5 squares up.
4. Plot the New Vertices: From point A, move the new calculated distances (horizontal and vertical) to plot the position of each new, enlarged vertex.
5. Connect the Points: Draw lines connecting the new vertices in the same order as the original shape to form the enlarged image.
Summary of Each Shape's Transformation:
* Shape 1 (Triangle, Scale Factor 2): The triangle will become twice as large. Each vertex will be twice as far from point A as it was originally.
* Shape 2 (Triangle, Scale Factor 4): The triangle will become four times larger. Each vertex will be four times as far from point A.
* Shape 3 (Square, Scale Factor 2): The square will become twice as wide and twice as tall. Its bottom edge will be twice as far from point A.
* Shape 4 (Diamond, Scale Factor 3): The diamond will become three times larger. Each vertex will be three times as far from point A.
* Shape 5 (Hexagon, Scale Factor 3): The hexagon will become three times larger. Its bottom vertex will be three times as far from point A.
* Shape 6 (L-shape, Scale Factor 2): The L-shape will become twice as large in all dimensions. Each corner will be twice as far from point A.
* Shape 7 (T-shape, Scale Factor 4): The T-shape will become four times larger. Each corner will be four times as far from point A.
* Shape 8 (Parallelogram, Scale Factor 1 1/2): The parallelogram will become 1.5 times larger. Each vertex will be 1.5 times as far from point A.
By following this method for each of the eight shapes, you will have successfully completed the task.
Parent Tip: Review the logic above to help your child master the concept of scale factor worksheet.
