Answer:
1. Reflection.
2. The scale factor is [tex]-\frac{1}{4}[/tex].
3. The coordinates of A' are (-9,4).
Step-by-step explanation:
1. The hexagon on the right is the image of the hexagon on the left.
Both figures has same size and shape. The graph is symmetrical about the y-axis. Therefore the graph is reflected about the y-axis.
Hence, the correct option is 4.
2. The given dilation is
[tex]D_o,k=(20,16)\rightarrow (-5,-4)[/tex]
The scale factor is
[tex]k=\frac{\text{x-coordinate of image}}{\text{x-coordinate of preimage}}[/tex]
[tex]k=\frac{-5}{20}[/tex]
[tex]k=-\frac{1}{4}[/tex]
The scale factor is [tex]-\frac{1}{4}[/tex].
3. The point A (3, 4) is reflected over the line x = 2, and then is reflected over the line x = -4.
If a point reflected over the line x = 2, then
[tex](x,y)\rightarrow (4-x,y)[/tex]
[tex](3,4)\rightarrow (4-3,4)=(1,4)[/tex]
If a point reflected over the line x = -4, then
[tex](x,y)\rightarrow (-x-8,y)[/tex]
[tex](1,4)\rightarrow (-1-8,4)=(-9,4)[/tex]
Therefore the coordinates of A' are (-9,4).
