T has points (2,1)(3,-2)(1,-1)
E1 has a scale factor of 3 and its Centre of Enlargement is (0,0). E2 has a scale factor of 0.5 and its centre of enlargement is (0,0).
I know how to do those, my question is how do you do E2E1 with a scale factor of 1.5 and centre of enlargement (0,0)?
or E1E2-scale factor of 1.5 and centre of enlargement (0,0)?
To find the transformation E2E1 with a scale factor of 1.5 and centre of enlargement (0,0), you need to perform the transformations in the correct order.
Step 1: Perform E1 transformation with a scale factor of 1.5 and centre of enlargement (0,0).
To apply the E1 transformation with a scale factor of 1.5, you multiply the coordinates of each point by 1.5. Since the centre of enlargement is (0,0), the points remain at the same location relative to the origin.
For each point (x, y), the new coordinates after the E1 transformation would be:
(x_new, y_new) = (1.5 * x, 1.5 * y)
Applying this to the points (2, 1), (3, -2), (1, -1):
(2_new, 1_new) = (1.5 * 2, 1.5 * 1) = (3, 1.5)
(3_new, -2_new) = (1.5 * 3, 1.5 * -2) = (4.5, -3)
(1_new, -1_new) = (1.5 * 1, 1.5 * -1) = (1.5, -1.5)
Step 2: Perform E2 transformation with a scale factor of 1.5 and centre of enlargement (0,0).
To apply the E2 transformation with a scale factor of 1.5, you multiply the coordinates of each point by 1.5. Since the centre of enlargement is (0,0), the points remain at the same location relative to the origin.
For each point (x, y), the new coordinates after the E2 transformation would be:
(x_new, y_new) = (1.5 * x, 1.5 * y)
Applying this to the points obtained from the E1 transformation:
(3_new, 1.5_new) = (1.5 * 3, 1.5 * 1.5) = (4.5, 2.25)
(4.5_new, -3_new) = (1.5 * 4.5, 1.5 * -3) = (6.75, -4.5)
(1.5_new, -1.5_new) = (1.5 * 1.5, 1.5 * -1.5) = (2.25, -2.25)
Therefore, the result of the transformation E2E1 with a scale factor of 1.5 and centre of enlargement (0,0) is:
(4.5, 2.25), (6.75, -4.5), (2.25, -2.25).
To find the transformation E1E2 with a scale factor of 1.5 and centre of enlargement (0,0), you would follow the same steps as above but perform the E2 transformation first and then the E1 transformation.