Question

enlargement
reduction
what is the scale factor? *
1 point
1/4
1/2
2
3
4
if c= (-8,4) what is the coordinate of c? *
1 point
(9,3)
(6,2)
(-2,1)
(-2,-1)

Explanation:

Step1: Identify transformation type

The image $\triangle A'B'C'$ is smaller than $\triangle ABC$, so it is a reduction.

Step2: Find scale - factor

Let's consider the distance between corresponding points. For example, if we look at the horizontal and vertical displacements of corresponding points, we can see that the side - lengths of $\triangle A'B'C'$ are $\frac{1}{4}$ of the side - lengths of $\triangle ABC$. So the scale factor is $\frac{1}{4}$.

Step3: Calculate new coordinates

If the scale factor $k=\frac{1}{4}$ and the original point $C=(-8,4)$, the new coordinates of $C'$ are obtained by multiplying the coordinates of $C$ by the scale factor. $x_{C'}=\frac{1}{4}\times(-8)=-2$ and $y_{C'}=\frac{1}{4}\times4 = 1$. So $C'=(-2,1)$.

Answer:

1. Reduction
2. $\frac{1}{4}$
3. $(- 2,1)$