Question

Identify the matrix transformation of △ DEF , which has coordinates D(3,-2), E(4,1) , and F(7,2) , for a translation 1 unit left and 2 units up. Then identify the correct vertices of the image.

A. [3 4 7] + [1 1 1] = [4 5 8] D(4,-4) , E(s,-1) , F (8,0)
[-2 1 2] [-2 -2 -2] [-4 -1 0]

B. [3 4 7] + [1 1 1] = [4 5 8] D(4,0) , E(5,3) , F (8,4)
[-2 -1 2] [2 2 2] [0 3 4]

C. [3 4 7] + [-1 -1 -1] = [2 3 6] D(2,-4) , E(3,-1) , F (6,0)
[-2 1 2] [-2 -2 -2] [-4 -1 0]

D. [3 4 7] + [-1 -1 -1] = [2 3 6] D(2,0) , E(3,3) , F (6,4)
[-2 1 2] [2 2 2] [0 3 4]

Answer 1

The matrix transformation and the vertices of the image is
`\left[\begin{array}{ccc}3&4&7\\-2&1&2\end{array}\right] + \left[\begin{array}{ccc}-1&-1&-1\\2&2&2\end{array}\right] = \left[\begin{array}{ccc}2&3&6\\0&3&4\end{array}\right]`

D'(2,0), E'(3,3) , and F'(6,4)

Identifying the matrix transformation and the vertices of the image.

From the question, we have the following parameters that can be used in our computation:

D(3,-2), E(4,1) , and F(7,2)

When represented as a matrix, we have

`\left[\begin{array}{ccc}3&4&7\\-2&1&2\end{array}\right]`

Also, we have the transformation to be

A translation 1 unit left and 2 units up.

This is represented as

`\left[\begin{array}{ccc}-1&-1&-1\\2&2&2\end{array}\right]`

So, we have the following equation

`\left[\begin{array}{ccc}3&4&7\\-2&1&2\end{array}\right] + \left[\begin{array}{ccc}-1&-1&-1\\2&2&2\end{array}\right]`

Evaluate the sum

`\left[\begin{array}{ccc}3&4&7\\-2&1&2\end{array}\right] + \left[\begin{array}{ccc}-1&-1&-1\\2&2&2\end{array}\right] = \left[\begin{array}{ccc}2&3&6\\0&3&4\end{array}\right]`

Hence, the matrix transformation and the vertices of the image is
`\left[\begin{array}{ccc}3&4&7\\-2&1&2\end{array}\right] + \left[\begin{array}{ccc}-1&-1&-1\\2&2&2\end{array}\right] = \left[\begin{array}{ccc}2&3&6\\0&3&4\end{array}\right]`

And, we have

D'(2,0), E'(3,3) , and F'(6,4)