Question

1. The hexagon on the right is the image of the hexagon on the left.

What transformation would result in this image?
(photo 1)

2. Given a dilation around the origin, what is the scale factor K?
D o, K = (20,16) → (-5,-4)
(photo 2)

3. The point A (3, 4) is reflected over the line x = 2, and then is reflected over the line x = -4. What are the coordinates of A'?
(photo 3)

Answer 1

1st one is rotation
2nd one is -1/4
3rd one is -9,4

Answer 2

1. Reflection.

2. The scale factor is
`-(1)/(4)`.

3. The coordinates of A' are (-9,4).

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

`D_o,k=(20,16)\rightarrow (-5,-4)`

The scale factor is

`k=\frac{\text{x-coordinate of image}}{\text{x-coordinate of preimage}}`

`k=(-5)/(20)`

`k=-(1)/(4)`

The scale factor is
`-(1)/(4)`.

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

`(x,y)\rightarrow (4-x,y)`

`(3,4)\rightarrow (4-3,4)=(1,4)`

If a point reflected over the line x = -4, then

`(x,y)\rightarrow (-x-8,y)`

`(1,4)\rightarrow (-1-8,4)=(-9,4)`

Therefore the coordinates of A' are (-9,4).