Problem 2 Finding a Dilation Image

What are the images of the vertices of Δ P Z G cap delta p z g  for a dilation with center (0, 0) and scale factor 2? Graph the image of Δ P Z G . cap delta p z g .

Identify the coordinates of each vertex. The center of dilation is the origin and the scale factor is 2, so use the dilation rule ( x , y ) → ( 2 x , 2 y ) . open x comma y close rightwards arrow open 2 x comma 2 y close .

P ( 2 , 0 ) → ( 2 · 2 , 2 · 0 ) , or  P ′ ( 4 , 0 ) . Z ( − 3 , 1 ) → ( 2 · ( − 3 ) , 2 · 1 ) , or  Z ′ ( − 6 , 2 ) . G ( 0 , − 2 ) → ( 2 · 0 , 2 · ( − 2 ) ) , or  G ′ ( 0 , − 4 ) . table with 3 rows and 1 column , row1 column 1 , p open 2 comma 0 close rightwards arrow open 2 middle dot 2 comma 2 middle dot 0 close comma or , p prime , open 4 comma 0 close . , row2 column 1 , z open negative 3 comma 1 close rightwards arrow open 2 middle dot open negative 3 close comma 2 middle dot 1 close comma or , z prime , open negative 6 comma 2 close . , row3 column 1 , g open 0 comma negative 2 close rightwards arrow open 2 middle dot 0 comma 2 middle dot open negative 2 close close comma or , g prime , open 0 comma negative 4 close . , end table

To graph the image of Δ P Z G , cap delta p z g comma  graph P ′ , Z ′ , and  G ′ . p prime , comma , z prime , comma , and , g prime , .  Then draw Δ P ′ Z ′ G ′ . cap delta , p prime , z prime , g prime , .

✓ Got It?

2. 1. What are the images of the vertices of Δ P Z G cap delta p z g  for a dilation with center (0, 0) and scale factor 1 2 ? 1 half , question mark
   2. Reasoning In Problem 2, how can you prove Δ P ′ Z ′ G ′ ∼ Δ P Z G cap delta , p prime , z prime , g prime , tilde operator cap delta p z g  using a postulate or theorem from Chapter 7?

Problem 3 Using a Scale Factor to Find a Length

Biology A magnifying glass shows you an image of an object that is 7 times the object's actual size. So the scale factor of the enlargement is 7. The photo shows an apple seed under this magnifying glass. What is the actual length of the apple seed?

1.75 = 7 · p image length = scale factor · actual length 0.25 = p Divide each side by  7 . table with 2 rows and 4 columns , row1 column 1 , 1.75 , column 2 equals , column 3 7 middle dot p , column 4 imagelength . equals . scalefactor . middle dot . actuallength , row2 column 1 , 0.25 , column 2 equals , column 3 p , column 4 cap divideeachsideby . 7 . , end table

The actual length of the apple seed is 0.25 in.

✓ Got It?

3. The height of a document on your computer screen is 20.4 cm. When you change the zoom setting on your screen from 100% to 25%, the new image of your document is a dilation of the previous image with scale factor 0.25. What is the height of the new image?