Question

Polygon ABCD with A (0,4), B (-4, 8), C (3, 3), and D (4, -2), is dilated by a scale factor of /2. What are the new coordinates? Is this a reduction or enlargement? *

Answer 1

The formula for dilations with center at origin is

$\begin{gathered} D_{O,k}(x,y)=(kx,ky) \\ \text{ Where O is the center of dilation at (0,0) and} \\ k\text{ is the scale factor} \end{gathered}$

Likewise when

*k > 1, the dilation is an enlargement

*k < 1, the dilation is a reduction

*k = 1, the dilation is a congruence

So, in this case, you have

$k=\frac{1}{2}<1$

Then, the dilation of the polygon is a reduction.

Now, finding the new coordinates of the polygon, you have

$\begin{gathered} A(0,4)\rightarrow A^{\prime}(\frac{1}{2}\cdot0,\frac{1}{2}\cdot4)=A^{\prime}(0,2) \\ \end{gathered}$$B(-4,8)\rightarrow B^{\prime}(\frac{1}{2}\cdot-4,\frac{1}{2}\cdot8)=B^{\prime}(-2,4)$

$C(3,3)\rightarrow C^{\prime}(\frac{1}{2}\cdot3,\frac{1}{2}\cdot3)=C^{\prime}(1.5,1.5)$

$D(4,-2)\rightarrow D^{\prime}(\frac{1}{2}\cdot4,\frac{1}{2}\cdot-2)=D^{\prime}(2,-1)$

Therefore, the correct answer is C. A'(0,2), B'(-2,4), C'(1.5,1.5), D'(2,-1): Reduction.