Respuesta :
Answer:
Option A.
Step-by-step explanation:
The vertices of square S are (0,0), (5,0), (5,-5) and (0,-5).
The vertices of square S' are (0,1), (0,3), (2,3) and (2,1).
It is given that center of dilation is (0,0). From the point it is clear that the distance between point of S and origin is greater that S'. It means the scale factor is less than 1.
If scale factor is 2/5, then
[tex](x,y)\to (\dfrac{2}{5}x,\dfrac{2}{5}y)[/tex]
[tex](0,0)\to (\dfrac{2}{5}(0),\dfrac{2}{5}(0))=(0,0)[/tex]
[tex](5,0)\to (\dfrac{2}{5}(5),\dfrac{2}{5}(0))=(2,0)[/tex]
[tex](5,-5)\to (\dfrac{2}{5}(5),\dfrac{2}{5}(-5))=(2,-2)[/tex]
[tex](0,-5)\to (\dfrac{2}{5}(0),\dfrac{2}{5}(-5))=(0,-2)[/tex]
If the figure translated 3 units up, then
[tex](x,y)\to (x,y+3)[/tex]
[tex](0,0)\to (0,0+3)=(0,3)[/tex]
[tex](2,0)\to (2,0+3)=(2,3)[/tex]
[tex](2,-2)\to (2,-2+3)=(2,1)[/tex]
[tex](0,-2)\to (0,-2+3)=(0,1)[/tex]
These are the vertices of square S'.
A dilation by a scale factor of two-fifths and then a translation of 3 units up are used to get square S' from S.
Therefore, the correct option is A.
