Question

use the rule (x,y) (x-2, y-4) to graph the image of the rectangle. Then describe the transformation.The coordinates of the vertices of the rectagle before the tansformation, are:A (1,1)B (4,1)C (4,-2)D(1, -2)

Answer 1

Use the given rule to find the coordinates of the transformed vertices:

`\begin{gathered} (x,y)\rightarrow(x-2,y-4) \\ \Rightarrow A(1,1)\rightarrow A^(\prime)(1-2,1-4)=A^(\prime)(-1,-3) \\ \Rightarrow B(4,1)\rightarrow B^(\prime)(4-2,1-4)=B^(\prime)(2,-3) \\ \Rightarrow C(4,-2)\rightarrow C^(\prime)(4-2,-2-4)=C^(\prime)(2,-6) \\ \Rightarrow D(1,-2)\rightarrow D^(\prime)(1-2,-2-4)=D^(\prime)(-1,-6) \end{gathered}`

Plot the points A,B,C,D,A',B',C' and D':

Identify that the transformation corresponds to a translation two units to the left and four units downwards: