Shape A is drawn on the grid below - OCR - GCSE Maths - Question 9 - 2017 - Paper 1

To enlarge shape A with a scale factor of 3 and a centre of enlargement at (0, 0), we need to apply the enlargement formula to each vertex of shape A. The formula for enlargement is:

$(x', y') = (k(x - c_x) + c_x, k(y - c_y) + c_y)$

where:

• $(x', y')$ are the coordinates of the enlarged shape
• $(x, y)$ are the original coordinates of the shape
• $k$ is the scale factor (3 in this case)
• $(c_x, c_y)$ is the centre of enlargement, which is (0, 0).

Step 1: Identify the vertices of Shape A

Assuming Shape A has the following vertices (example coordinates):

• Vertex 1: (1, 2)
• Vertex 2: (2, 3)
• Vertex 3: (3, 3)
• Vertex 4: (2, 1)

Step 2: Apply the enlargement formula to each vertex

1. For Vertex 1 (1, 2):

   • $x' = 3(1 - 0) + 0 = 3$
   • $y' = 3(2 - 0) + 0 = 6$ → New vertex (3, 6)

2. For Vertex 2 (2, 3):

   • $x' = 3(2 - 0) + 0 = 6$
   • $y' = 3(3 - 0) + 0 = 9$ → New vertex (6, 9)

3. For Vertex 3 (3, 3):

   • $x' = 3(3 - 0) + 0 = 9$
   • $y' = 3(3 - 0) + 0 = 9$ → New vertex (9, 9)

4. For Vertex 4 (2, 1):

   • $x' = 3(2 - 0) + 0 = 6$
   • $y' = 3(1 - 0) + 0 = 3$ → New vertex (6, 3)

Step 3: Final vertices of the enlarged shape A

• New Vertex 1: (3, 6)
• New Vertex 2: (6, 9)
• New Vertex 3: (9, 9)
• New Vertex 4: (6, 3)

Step 4: Plot the points

The enlarged shape A can now be plotted using the new vertices on the coordinate grid.