Question

triangle abc is a dilation of triangle abc. which of the following statements is not true? the scale factor of the dilation is 1/2 the figures are the same shape, but different sizes. the motion rule for the dilation is (x, y)→(2x, 2y). dilations with scale factors between 0 and 1 are reductions.

Explanation:

Step1: Analyze the scale - factor

The pre - image is $\triangle ABC$ and the image is $\triangle A'B'C'$. The distance between corresponding points (e.g., from $A$ to $A'$) shows that the image is smaller than the pre - image. If we consider a point $(x,y)$ in $\triangle ABC$ and its corresponding point in $\triangle A'B'C'$, the scale factor $k$ is such that the coordinates of the image of a point $(x,y)$ are $(kx,ky)$. Since the image is smaller, $k=\frac{1}{2}$.

Step2: Recall properties of dilation

Dilations create similar figures. Similar figures have the same shape but different sizes. When the scale factor $0 < k<1$, the dilation is a reduction.

Step3: Check the motion rule

If the scale factor $k = \frac{1}{2}$, the motion rule for the dilation should be $(x,y)\to(\frac{1}{2}x,\frac{1}{2}y)$, not $(x,y)\to(2x,2y)$.

Answer:

The motion rule for the dilation is $(x,y)\to(2x,2y)$.