Question

enlargement
reduction
what is the scale factor? *
1 point
1/3
1/2
2
3
4
if v = (0,6) what is the coordinate of v? *
1 point
(0,-6)
(0,-3)
(0,3)
(3,0)

Explanation:

Step1: Identify transformation type

The image of the polygon is smaller than the original, so it is a reduction.

Step2: Find scale - factor

Let's consider a side - length. For example, if we look at a vertical side of the original and new polygon. Suppose the length of a vertical side of the original polygon is 6 units and the length of the corresponding vertical side of the new polygon is 3 units. The scale factor $k=\frac{\text{length of new side}}{\text{length of original side}}=\frac{3}{6}=\frac{1}{2}$.

Step3: Calculate new coordinate

If the scale factor $k = \frac{1}{2}$ and the original coordinate of $V=(0,6)$, to find the new coordinate of $V'$, we multiply each coordinate by the scale factor. For the $x$ - coordinate: $x'=0\times\frac{1}{2} = 0$, for the $y$ - coordinate: $y'=6\times\frac{1}{2}=3$. So the coordinate of $V'$ is $(0,3)$.

Answer:

1. Reduction
2. $\frac{1}{2}$
3. $(0,3)$