1. We are given two orange rectangles A and B on a coordinate grid. Rectangle A has corners at approximately (1,1), (3,1), (3,2), and (1,2). Rectangle B has corners at approximately (-7,3), (-4,3), (-4,6), and (-7,6). 2. The problem asks to describe two different enlargements that map rectangle A onto rectangle B, specifying their scale factors and centres of enlargement. 3. To find the scale factor for each enlargement, calculate the ratio of corresponding sides of B to A. - Length of A's base: distance between (1,1) and (3,1) is $3-1=2$ units. - Length of B's base: distance between (-7,3) and (-4,3) is $-4 - (-7) =3$ units. - Length of A's height: distance between (1,1) and (1,2) is $2-1=1$ unit. - Length of B's height: distance between (-7,3) and (-7,6) is $6-3=3$ units. 4. From these measurements, the scale factor for an enlargement mapping A to B is $\frac{3}{2} = 1.5$ for the base and $\frac{3}{1} = 3$ for the height. However, since enlargements preserve ratio, the scale factors must be consistent. 5. This suggests the enlargements use different centres, resulting in two different scale factors for the mappings. 6. Based on the dashed enlargement lines shown (from outside the origin) and the approximate coordinates, two possible enlargements are: - First enlargement: scale factor $1.5$, centre approximately at $(-3,3)$. - Second enlargement: scale factor $3$, centre approximately at $(0,0)$ (the origin). 7. These values correspond to the two different transformations mapping rectangle A onto rectangle B. Final answers: Enlargement with a scale factor of $1.5$ and centre $(-3,3)$. Enlargement with a scale factor of $3$ and centre $(0,0)$. Graph shapes and their math in a sentence: Rectangle B is an enlargement of rectangle A by scale factors 1.5 and 3, with centres of enlargement at $(-3,3)$ and the origin respectively, mapping corresponding points via straight lines through these centres and scaling distances accordingly.