Enlarging a Shape with a Negative Scale FactorA shape can be enlarged with a negative scale factor. If the scale factor is negative, the shape is enlarged on the other side of the centre of enlargement and it is turned upside down.
How to Enlarge a Shape with a Negative Scale FactorEnlarging a shape with a negative scale factor is easy.
QuestionEnlarge the shape below by a scale factor of −2 about the centre of enlargement (5, 5).
Draw a line from point A to the centre of enlargement.Note: It is useful to extend the line beyond the centre of enlargement.
Measure the length of the line from the point to the centre of enlargement. In our example, the point is 1 diagonal unit from the centre of enlargement (or 1 unit across and 1 up).
Multiply this distance (2) by the scale factor. Ignore the − sign in front of the scale factor for now.The distance to the transformed point is 2 diagonal units. Now we use the − sign in the scale factor. Because the scale factor is negative, the distance will be on the other side of the centre of enlargement. The 2 diagonal units will be 2 units to the left and 2 units down.
Scaled distance = Distance × Scale factor
Scaled distance = 1 diagonal units × 2
Scaled distance = 2 diagonal units
Measure the distance found in Step 4 along the line drawn in Step 2. Measure it from the centre of enlargement going away from the shape. This is the point on the enlarged shape, which we will call A'.
Answer:With all the vertices (corners) of the shape transformed, the enlarged shape can be drawn:
By multiplying the shape by a scale factor of −2, the enlarged shape is 2 times larger and 2 times the distance from the centre of enlargement. It is also the other side of the centre of enlargement and turned upside down.