Two-dimensional proportional change
Two dimensions multiplied by the same scale factor
Two-dimensional proportional change refers to the change in size or dimensions of an object, with respect to two parameters or variables, while maintaining the same proportion between them. For instance, if we have a rectangle with dimensions of 4 units by 6 units and we change it proportionally by a factor of 2, then its new dimensions will be 8 units by 12 units. This means that the changes in the width and height of the rectangle are proportional, with both of them increasing by a factor of 2.
To calculate the proportional change in a two-dimensional object, we need to identify the scaling factor, which is the ratio of the new size to the original size. We can then multiply the original size by the scaling factor to obtain the new size.
For example, if we have a square with a side length of 10 cm and it is scaled up proportionally by a factor of 1.5, its new side length will be:
Scaling factor = New size/Original size = 1.5
New size = Scaling factor x Original size
New size = 1.5 x 10 cm = 15 cm
Therefore, the proportional change in the square is an increase in size by 50%.
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