Question

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

Explanation:

Step1: Identify transformation type

The image of $\triangle GHI$ (the large - sized triangle) is $\triangle G'H'I'$ (the small - sized triangle). Since the new figure $\triangle G'H'I'$ is smaller than the original $\triangle GHI$, it is a reduction.

Step2: Find scale factor

Let's consider a side - length. For example, if we look at the horizontal distance of a side. Suppose we consider the horizontal distance between two corresponding points. If the original length is $l$ and the new length is $l'$, and we can observe from the graph that the new length is half of the original length. So the scale factor $k=\frac{1}{2}$.

Step3: Find coordinates of $G'$

If the scale factor $k = \frac{1}{2}$ and the original point $G=(-2,-2)$, to find the coordinates of the new point $G'$, we use the rule for dilation $(x,y)\to(kx,ky)$. Substituting $x=-2,y = - 2,k=\frac{1}{2}$, we get $x'=\frac{1}{2}\times(-2)=-1$ and $y'=\frac{1}{2}\times(-2)=-1$. So the coordinates of $G'$ are $(-1,-1)$.

Answer:

1. Reduction
2. 1/2
3. (-1,-1)