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 perform the composition of two enlargements, we must first find the new coordinates of each point after applying the first enlargement, and then apply the second enlargement to those new coordinates.
To solve E2E1 with a scale factor of 1.5 and a centre of enlargement at (0,0), follow these steps:
1. Apply the first enlargement, E1, to each coordinate of point T as follows:
- Multiply each coordinate by the scale factor of E1 (which is 3).
- For the first point (2,1), the new coordinates would be (2*3, 1*3) = (6, 3).
- For the second point (3,-2), the new coordinates would be (3*3, -2*3) = (9, -6).
- For the third point (1,-1), the new coordinates would be (1*3, -1*3) = (3, -3).
2. Apply the second enlargement, E2, to the new coordinates obtained from step 1 as follows:
- Multiply each coordinate by the scale factor of E2 (which is 0.5).
- For the new coordinates (6,3), the new coordinates after E2 would be (6*0.5, 3*0.5) = (3, 1.5).
- For the new coordinates (9,-6), the new coordinates after E2 would be (9*0.5, -6*0.5) = (4.5, -3).
- For the new coordinates (3,-3), the new coordinates after E2 would be (3*0.5, -3*0.5) = (1.5, -1.5).
Therefore, the composition E2E1 with a scale factor of 1.5 and a centre of enlargement at (0,0) would result in the new points (3, 1.5), (4.5, -3), (1.5, -1.5).
To perform the composition E1E2 with a scale factor of 1.5 and a centre of enlargement at (0,0), simply follow the same steps as above but in reverse order.