Question

identify the transformation in the diagram below by the correct rule in vector form: identifique la transformación en el diagrama de abajo por la regla correcta en forma vectorial: answer (respuesta) type your answer_

Explanation:

Step1: Observe x - coordinate change

For point A, if its original x - coordinate is \(x_1\) and new x - coordinate is \(x_2\), by counting the grid squares, we find that the x - coordinate of each point in the original figure is increased by 3. For example, if \(A=(1, - 1)\) and \(A'=(4,-1)\), \(4=1 + 3\).

Step2: Observe y - coordinate change

For point A, if its original y - coordinate is \(y_1\) and new y - coordinate is \(y_2\), by counting the grid squares, we find that the y - coordinate of each point in the original figure is decreased by 1. For example, if \(A=(1, - 1)\) and \(A'=(4,-1)\), \(-1=-1-0\) (in general, for all points \(y_2=y_1 - 1\)).

Step3: Write the transformation in vector form

The transformation rule in vector form for a point \((x,y)\) to \((x',y')\) is \(

$$\begin{pmatrix}x'\\y'\end{pmatrix}$$

=

$$\begin{pmatrix}x\\y\end{pmatrix}$$

+

$$\begin{pmatrix}3\\- 1\end{pmatrix}$$

\)

Answer:

\(

$$\begin{pmatrix}x'\\y'\end{pmatrix}$$

=

$$\begin{pmatrix}x\\y\end{pmatrix}$$

+

$$\begin{pmatrix}3\\-1\end{pmatrix}$$

\)