Question

Derive the composite transformations that

1. Scale an object about the fix point (h,k)

2. Rotate an object about the fix point (h,k)

3. Reflects an object about a arbitrary axis L: y=m*x+b.​

Answer 1

Answer:

the story of vill the rise of napoleon the rise of napoleon the rise of napoleon the class is changed to the class so teacher did not say hello to all the best for you to the class so teacher did not say

Answer 2

Composite transformation:

Explanation:

• A composite transformation is when two or more transformations are performed on a figure to produce a new figure.

• The formula for scaling of an object about the fixpoint (h,k) is

      S(h,k) = $\left[\begin{array}{ccc}1&0&h\\0&1&k\\0&0&1\end{array}\right]$

• The formula for rotating an object about the fixpoint (h,k) is

    R(h,k) = $\left[\begin{array}{ccc}S_x&0&0\\0&S_y&0\\0&0&1\end{array}\right]$

• The formula for reflecting an object about an arbitrary axis L: y=m*x+b is

    r(h,k) = $\left[\begin{array}{ccc}1&1&-h\\0&1&-k\\0&0&1\end{array}\right]$

• The composite transformation is the product of scaling, rotating, and reflection.

        T = S × R × r

           =  $\left[\begin{array}{ccc}1&0&h\\0&1&k\\0&0&1\end{array}\right]$    ×   $\left[\begin{array}{ccc}S_x&0&0\\0&S_y&0\\0&0&1\end{array}\right]$    ×   $\left[\begin{array}{ccc}1&1&-h\\0&1&-k\\0&0&1\end{array}\right]$

        T = $\mahbf{{\left[\begin{array}{ccc}S_x&0&-hS_x+h\\0&S_y&-kS_y+k\\0&0&1\end{array}\right]}}$