Question

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

Answer 1

Reflection across the x-axis followed by dilation by a scale factor of
`(1)/(4)` with the center of dilation at the origin

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
`(1)/(4)` with the center of dilation at the origin. This transformation has the rule

`(x,y)\rightarrow ((1)/(4)x,(1)/(4)y)`

Thus,

• 
  `E''(-6,-8)\rightarrow E'(-(3)/(2),-2);`
• 
  `F''(0,-8)\rightarrow F'(0,-2);`
• 
  `G''(0,-1)\rightarrow G'(0,-(1)/(4));`
• 
  `D''(-6,-1)\rightarrow D'(-(3)/(2),-(1)/(4)).`

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