Question

Describe a sequence of transformations that exhibits the similarity between the pair of figures shown.

Answer 1

Answer:

Reflection across the x-axis followed by dilation by a scale factor of $\frac{1}{4}$ with the center of dilation at the origin

Step-by-step explanation:

Rectangle EFGD has vertices at points E(-6,8), F(0,8), G(0,1) and D(-6,1).

1 transformation - reflection across the x-axis with the rule

$(x,y)\rightarrow (x,-y)$

So, the image rectangle E''F''G''D'' has vertices with coordinates

• $E(-6,8)\rightarrow E''(-6,-8);$
• $F(0,8)\rightarrow F''(0,-8);$
• $G(0,1)\rightarrow G''(0,-1);$
• $D(-6,1)\rightarrow D''(-6,-1).$

2 transformation - dilation by a scale factor of $\frac{1}{4}$ with the center of dilation at the origin. This transformation has the rule

$(x,y)\rightarrow (\frac{1}{4}x,\frac{1}{4}y)$

Thus,

• $E''(-6,-8)\rightarrow E'(-\frac{3}{2},-2);$
• $F''(0,-8)\rightarrow F'(0,-2);$
• $G''(0,-1)\rightarrow G'(0,-\frac{1}{4});$
• $D''(-6,-1)\rightarrow D'(-\frac{3}{2},-\frac{1}{4}).$

These are exactly vertices of rectangle E'F'G'D'.