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Sagot :
Transforming a shape involves changing the size and/or the location of the shape.
- The rule that will take the triangle to a congruent triangle is [tex](x,y) \to (x,-y)[/tex]
- The rule that will take the triangle to a figure that is similar is [tex](x,y) \to (0.5x,0.5y)[/tex].
- The rule that will take the triangle to a figure that is not similar or congruent is [tex](x,y) \to (0.5x,2y)[/tex].
Rigid transformation
When a shape is transformed by a rigid transformation, then the image of the shape will be congruent to the original shape.
An example of a rigid transformation is a reflection over the x-axis; and the rule is:
[tex](x,y) \to (x,-y)[/tex]
So, a rule that will take the triangle to a congruent triangle is [tex](x,y) \to (x,-y)[/tex]
Nonrigid transformation
When a shape is transformed by a nonrigid transformation, then the image of the shape will not be congruent to the original shape, however the original shape and the transformed shape would be similar
An example of a nonrigid transformation is a dilation by a scale factor od 0.5; and the rule is:
[tex](x,y) \to (0.5x,0.5y)[/tex]
So, a rule that will take the triangle to a figure that is similar is [tex](x,y) \to (0.5x,0.5y)[/tex]
However, if the x and y coordinates of the shape are dilated by different scale factors, then the resulting shape would neither be similar nor be congruent to the original shape.
A rule that will take the triangle to a figure that is not similar or congruent is [tex](x,y) \to (0.5x,2y)[/tex].
Read more about transformation at:
https://brainly.com/question/4289712
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