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Complete the table, and determine the rule for this transformation.
| input | output |
|---|---|
| \((2,\text-3)\) | \((\text-3,2)\) |
| \((4,5)\) | \((5,4)\) |
| \((0,4)\) | \((4,0)\) |
| \((1,6)\) | |
| \((\text-1,\text-2)\) | |
| \((x,y)\) |
Write a rule that describes this transformation.
| original figure | image |
|---|---|
| \((5,1)\) | \((2,\text-1)\) |
| \((\text-3,4)\) | \((\text-6,\text-4)\) |
| \((1,\text-2)\) | \((\text-2,2)\) |
| \((\text-1,\text-4)\) | \((\text-4,4)\) |
Select all the transformations that produce congruent images.
dilation
horizontal stretch
reflection
rotation
translation
Here are some transformation rules. For each transformation, first predict what the image of triangle \(ABC\) will look like. Then compute the coordinates of the image and draw it.
Reflect triangle \(ABC\) over the line \(x=\text-2\). Call this new triangle \(A’B’C’\). Then reflect triangle \(A’B’C’\) over the line \(x=0\). Call the resulting triangle \(A''B''C''\).
Describe a single transformation that takes \(ABC\) to \(A''B''C''\).
In the construction, \(A\) is the center of one circle, and \(B\) is the center of the other.
Explain why segments \(AC\), \(BC\), \(AD\), \(BD\), and \(AB\) have the same length.