Chapter 4.4, Problem 3CYU

To determine

To find: The correct option.

Answer to Problem 3CYU

The correct option is A.

Explanation of Solution

Given:

The given vertices of the rectangle is $R\left(-3,2\right),S\left(1,2\right),T\left(-3,-1\right)$ and $U\left(1,-1\right)$ .

The translated vertices is $\left(-4,1\right)$ .

Calculation:

Consider the given vertices is,

  $R\left(-3,2\right),S\left(1,2\right),T\left(-3,-1\right),U\left(1,-1\right)$

Consider the translational matrix is,

  $\left[\begin{array}{c}-3\\ -1\end{array}\right]+\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{c}-4\\ 1\end{array}\right]$

From above, the value of $x$ is,

  $\begin{array}{l}-3+x=-4\\ x=-4+3\\ x=-1\end{array}$

From above, the value of $y$ is,

  $\begin{array}{l}-1+y=1\\ y=2\end{array}$

The translational matrix is $\left[\begin{array}{c}-1\\ 2\end{array}\right]$ .

The rectangle RSTU is translated by adding -1 to the x coordinate and adding 2 to the y coordinate.

The coordinate of the vertices of the image is shown is,

  $\left[\begin{array}{cccc}-3& 1& -3& 1\\ 2& 2& -1& -1\end{array}\right]+\left[\begin{array}{cccc}-1& -1& -1& -1\\ 2& 2& 2& 2\end{array}\right]=\left[\begin{array}{cccc}-4& 0& -4& 0\\ 4& 4& 1& 1\end{array}\right]$

The coordinates of the vertices of the image are $R^{\prime }\left(-4,4\right),S^{\prime }\left(0,4\right),T^{\prime }\left(-4,1\right),U^{\prime }\left(0,1\right)$ .

Thus, the correct option is A.