A(-4,0) B(3,-3)
Dilation is a transformation that alters the size of a figure while maintaining its shape and proportions, which directly relates to similarity in geometry. When a figure undergoes dilation, the resulting image is similar to the original figure, meaning corresponding angles remain the same and corresponding sides are in proportion. This property of dilation ensures that similar shapes can be created by scaling up or down without distorting their fundamental characteristics. Thus, dilation is a key method for establishing similarity between geometric figures.
A translation of 4 units to the right followed by a dilation of a factor of 2
The input of a transformation on the coordinate plane is called the "preimage." The preimage is the original figure before any transformation, such as translation, rotation, reflection, or dilation, is applied to it. After the transformation, the resulting figure is referred to as the "image."
To write a rule for transformation, first identify the type of transformation you want to apply, such as translation, rotation, reflection, or dilation. Then, define the mathematical operation that corresponds to your transformation—for example, for a translation by a vector ( (a, b) ), the rule would be ( (x, y) \rightarrow (x + a, y + b) ). Finally, clearly state the initial coordinates and the resulting coordinates to complete the transformation rule.
Similarity.
Transformation
A similarity transformation uses a scale factor to enlarge or reduce the size of a figure while preserving its shape. It includes transformations such as dilation and similarity.
false
Dilation, rotation, reflection and translation
Non-examples of dilation would include transformations such as translation, rotation, and reflection. These transformations do not involve changing the size of the figure, only its position or orientation. Another non-example would be a similarity transformation, where the shape is resized proportionally but not dilated.
Dilation is a transformation that alters the size of a figure while maintaining its shape and proportions, which directly relates to similarity in geometry. When a figure undergoes dilation, the resulting image is similar to the original figure, meaning corresponding angles remain the same and corresponding sides are in proportion. This property of dilation ensures that similar shapes can be created by scaling up or down without distorting their fundamental characteristics. Thus, dilation is a key method for establishing similarity between geometric figures.
A translation of 4 units to the right followed by a dilation of a factor of 2
Dilation.
The input of a transformation on the coordinate plane is called the "preimage." The preimage is the original figure before any transformation, such as translation, rotation, reflection, or dilation, is applied to it. After the transformation, the resulting figure is referred to as the "image."
Dilation
Flexing is one such transformation.
To write a rule for transformation, first identify the type of transformation you want to apply, such as translation, rotation, reflection, or dilation. Then, define the mathematical operation that corresponds to your transformation—for example, for a translation by a vector ( (a, b) ), the rule would be ( (x, y) \rightarrow (x + a, y + b) ). Finally, clearly state the initial coordinates and the resulting coordinates to complete the transformation rule.