Enlarge triangle A by scale factor 2.5 with centre (0, 1) (Total for Question 9 is 2 marks) - Edexcel - GCSE Maths - Question 10 - 2019 - Paper 3

To enlarge triangle A by a scale factor of 2.5 centered at the point (0, 1), we follow these steps:

1. Identify the vertices of triangle A: Let's denote the vertices of triangle A as follows:

   • A(2, 2)
   • B(4, 2)
   • C(2, 4)

2. Calculate the enlargement for each vertex: The general formula for enlarging a point (x, y) with centre (cx, cy) and scale factor k is:

   $(x', y') = (cx + k \cdot (x - cx), cy + k \cdot (y - cy))$

   For scale factor k = 2.5 and centre (0, 1):

   • For A(2, 2):
     • $x' = 0 + 2.5 \cdot (2 - 0) = 5$
     • $y' = 1 + 2.5 \cdot (2 - 1) = 4$
     • A' = (5, 4)
   • For B(4, 2):
     • $x' = 0 + 2.5 \cdot (4 - 0) = 10$
     • $y' = 1 + 2.5 \cdot (2 - 1) = 3.5$
     • B' = (10, 3.5)
   • For C(2, 4):
     • $x' = 0 + 2.5 \cdot (2 - 0) = 5$
     • $y' = 1 + 2.5 \cdot (4 - 1) = 8.5$
     • C' = (5, 8.5)

3. Coordinates of the enlarged triangle: The vertices of the enlarged triangle A' are therefore:

   • A'(5, 4)
   • B'(10, 3.5)
   • C'(5, 8.5)

4. Draw the enlarged triangle: Plot the points A', B', and C' on the grid based on the calculated coordinates to visualize the result.