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AQA GCSE · Question 11 · Geometry and Measures
Describe fully the single transformation that maps shape A to shape B.
Describe fully the single transformation that maps shape A to shape B.
How to approach this question
1. **Identify the transformation type:** Shape B is smaller than shape A but has the same orientation, so it's an enlargement.
2. **Find the scale factor:** Pick a side on shape B and the corresponding side on shape A. Divide the length of the side on B by the length of the side on A. For example, the bottom side of B is 1 unit long, and the bottom side of A is 3 units long. So the scale factor is 1/3.
3. **Find the centre of enlargement:** Draw straight lines (ray lines) that pass through corresponding points on both shapes. For example, draw a line through the top-left corner of A and the top-left corner of B. Do this for at least one other pair of corresponding points. The point where these lines cross is the centre of enlargement.
Full Answer
The transformation is an enlargement.
To find the centre of enlargement, draw lines (rays) connecting corresponding vertices of the two shapes (e.g., top-right corner of A to top-right corner of B). The point where these lines intersect is the centre of enlargement. The lines from (2,5) to (3,-1), from (5,5) to (4,-1), and from (7,3) to (5,-2) all intersect at the point (1, -7).
To find the scale factor, compare the lengths of corresponding sides. The width of shape A is from x=2 to x=5, which is 3 units. The width of shape B is from x=3 to x=4, which is 1 unit. The scale factor is (image length) / (object length) = 1/3.
The transformation is an enlargement by scale factor 1/3, centre (1, -7).
To fully describe a transformation, you need to provide all the necessary details.
1. **Type of transformation:** Shape B is a different size to shape A, so it must be an enlargement.
2. **Scale Factor:** The scale factor is the ratio of a length on the new shape (image, B) to the corresponding length on the old shape (object, A).
- The length of the bottom edge of A is 5 - 2 = 3.
- The length of the bottom edge of B is 4 - 3 = 1.
- Scale Factor = Image Length / Object Length = 1 / 3.
3. **Centre of Enlargement:** To find the centre, we draw lines through corresponding points.
- Let's take the bottom-left point: A is at (2, 1), B is at (3, -1). A line through these points also passes through (1, -7).
- Let's take the bottom-right point: A is at (5, 1), B is at (4, -1). A line through these points also passes through (1, -7).
- Let's take the top point: A is at (7, 3), B is at (5, -2). A line through these points also passes through (1, -7).
Since all ray lines meet at (1, -7), this is the centre of enlargement.
The full description is: **Enlargement, scale factor 1/3, centre (1, -7).**
Common mistakes
✗ Forgetting one of the three key pieces of information (type, scale factor, centre).
✗ Getting the scale factor upside down (e.g., 3 instead of 1/3).
✗ Stating it's a negative enlargement because the shape has moved "across" the centre. The orientation is the same, so the scale factor is positive.
✗ Incorrectly identifying the centre of enlargement.
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