We have a triangle GHS which will be transformed by a dilation by a factor of 2, with center at (0,0) and a translation of (-3,1).
We can find the coordinates of a point (x,y) after the dilation of factor 2 as:
[tex]P=(x,y)\longrightarrow P^{\prime}=(2x,2y)[/tex]
Then, the translation can be described as:
[tex]P^{\prime}=(2x,2y)\longrightarrow P^{\prime}^{\prime}=(2x-3,2y+1)[/tex]
Then, for points G(3,1), H(5,3) and S(1,4), the transformations will result in:
[tex]\begin{gathered} G=(3,1)\longrightarrow G^{\prime\prime}=(2\cdot3-3,2\cdot1+1)=(3,3) \\ H=(5,3)\longrightarrow H^{\prime\prime}=(2\cdot5-3,2\cdot3+1)=(7,7) \\ S=(1,4)\longrightarrow S^{\prime\prime}=(2\cdot1-3,2\cdot4+1)=(-1,9) \end{gathered}[/tex]
We can see the transformation in the graph as:
Answer:
Coordinates after the transformation:
G''=(3,3)
H''=(7,7)
S''=(-1,9)
