Question

enlargement or reduction?
options: enlargment, reduction
what is the scale factor?

Explanation:

First Sub - Question (Enlargement or Reduction)

Step1: Compare Sizes

The original triangle (black) and the image triangle (red) are compared. The red triangle is smaller than the black one.

Step2: Determine Transformation

A reduction is a transformation where the image is smaller than the original figure. Since the red triangle ($A'B'C'$) is smaller than the black triangle ($ABC$), it is a reduction.

Step1: Identify Corresponding Sides

Let's consider the horizontal or vertical distance between corresponding points. For example, the distance from $A$ to $B$ (or other corresponding sides) in the original triangle and the image triangle.

Step2: Calculate Scale Factor

The scale factor $k$ is given by the ratio of the length of a side of the image to the length of the corresponding side of the original. By visually inspecting the grid, if we assume the original triangle has a side length (say from $A$ to a point) of 2 units (for example) and the image has a side length of 1 unit, the scale factor $k=\frac{1}{2}$. (We can also check the distance from the center of dilation $P$. The distance from $P$ to $A'$ and $P$ to $A$: if $PA = 6$ units and $PA'=3$ units, then the scale factor is $\frac{PA'}{PA}=\frac{3}{6}=\frac{1}{2}$)

Answer:

Reduction (the option with "Reduction" text)

Second Sub - Question (Scale Factor)