Final answer:
The question involves mathematics, specifically transformation geometry, as it refers to the enlargement of a shape using a scale factor of -2. To create an enlargement with such a scale factor, each point of the original shape must be mapped through the centre of enlargement to a point that is twice the distance on the opposite side, resulting in an enlarged, inverted image.
Step-by-step explanation:
The question asks about an enlargement of a geometric shape with a scale factor of -2 using a point x as the centre.
This concerns transformation geometry, specifically the concepts of enlargement and scale factors in Mathematics.
An enlargement with a negative scale factor like -2 means that the image will be scaled by a factor of 2 but will be on the opposite side of the centre point compared to the original object and it will be inverted.
To perform this transformation, you would take each vertex of shape M, draw a line from point x through the vertex, and then extend that line so that it is twice as long on the opposite side of the centre point, x.
This would effectively 'flip' the shape over the centre point, enlarging it by a factor of 2 and creating an inverted image.
For instance, if we consider enlargement of a square with side 1 unit through a scale factor of -2, each side of the square in the enlarged shape would be 2 units long.
If the original square was positioned with its bottom left vertex at point x, then the enlarged square would have its top right vertex at point x, and it would be inverted as well as enlarged.