Write the rule for the composition transformation (4 points)

Answer 1

In mathematics, specifically in the context of transformations in geometry, the composition transformation refers to the application of two or more transformations in sequence to an object. The general rule for a composition transformation can be expressed as follows:

1. Identify the Transformations: First, determine what transformations you are going to apply. Common transformations include translations, rotations, reflections, and dilations.

2. Order of Transformations: The order in which you apply the transformations matters. If you perform transformation A followed by transformation B, the notation would be \( B(A(\text{Point})) \).

3. Mathematical Representation: If \( T_1 \) and \( T_2 \) are two transformations, the composition of these transformations is denoted as \( T_2 \circ T_1 \). This means you first apply \( T_1 \) and then apply \( T_2 \) to the result of \( T_1 \).

4. Example: If you have a point \( P(x, y) \):

   • If \( T_1 \) is a translation by \( (a, b) \): \( T_1(P) = (x + a, y + b) \)
   • If \( T_2 \) is a rotation by an angle \( \theta \): Apply this transformation to the result of \( T_1 \).

In conclusion, the rule of composition transformation combines multiple transformations into a single transformation, where the result depends on the sequence in which you apply each transformation.

Answer 2

(x - ?, y - ?)

Answer 3

It seems you're looking for a specific structure related to a transformation in geometry, likely involving a translation. The form \((x - ?, y - ?)\) typically represents a translation transformation.

If you want to express a translation of a point \((x, y)\) by a vector \((a, b)\), the general rule would look like this:

\[ (x - a, y - b) \]

Here, \(a\) represents the horizontal shift (how much to move left or right), and \(b\) represents the vertical shift (how much to move up or down).

• If you move to the right, \(a\) is positive.
• If you move to the left, \(a\) is negative.
• If you move up, \(b\) is positive.
• If you move down, \(b\) is negative.

So, to fill in the blanks you provided:

• \( ? = a \) (if we are moving along the x-axis)
• \( ? = b \) (if we are moving along the y-axis)

The complete transformation would then be expressed as:

\[ (x - a, y - b) \]

If you have specific values for the translation, you can replace \(a\) and \(b\) with those values.