The given scale factors -2 and -9 represent reflections and expansions, 1.5 represents an expansion, and 1/4 represents a contraction. The sign of the scale factor indicates reflection (if negative), and the absolute value of the scale factor determines whether the dilation is an expansion (>1) or contraction (<1).
In geometry, dilation is a transformation that alters the size of a figure without changing its shape. It can either be an expansion (increase in size) or a contraction (decrease in size), depending on the scale factor. The scale factor is a number which scales, or multiplies, some quantity.
In the given problem, there are four scale factors: -2, 1.5, 1/4, and -9.
- A scale factor of -2 indicates a reflection and an expansion by a factor of 2.
- A scale factor of 1.5 indicates an expansion by a factor of 1.5.
- A scale factor of 1/4 indicates a contraction by a factor of 4.
- A scale factor of -9 indicates a reflection and a significant expansion by a factor of 9.
In general, a positive scale factor greater than 1 results in an expansion, while a positive scale factor less than 1 leads to a contraction. A negative scale factor indicates a reflection along with dilation. The absolute value of the scale factor determines whether the dilation is an expansion (absolute value > 1) or a contraction (absolute value < 1).