Question

assignment: page 96
natasha has a photo of a lasagna dish she made, which she wants to post to various
websites. the original image has a width of 300 pixels and a height of 450 pixels.
consider each set of new dimensions or scale percents that show adjustments to this
original image. describe how the image changed and whether the new image is
similar to the original. show your work and explain your reasoning.
a) new image: 360 pixels width, 540 pixels height
b) new image: 35% width, 35% height
c) new image: 150 pixels width, 150 pixels height

10 fill in the blank 2 points
a. the new image is choose your answer...
the original image was choose your answer... by a scale factor of type your answer...

11 fill in the blank 2 points
b. the new image is choose your answer...
the scale factor is choose your answer...

Explanation:

Part a (New Image: 360 pixels width, 540 pixels height)

Step1: Find scale factor for width

To find the scale factor, divide new width by original width. Original width = 300, new width = 360. So, scale factor for width: $\frac{360}{300} = 1.2$.

Step2: Find scale factor for height

Divide new height by original height. Original height = 450, new height = 540. So, scale factor for height: $\frac{540}{450} = 1.2$.

Step3: Determine similarity

Since both width and height have the same scale factor (1.2), the new image is similar to the original. The original image was enlarged by a scale factor of 1.2.

Step1: Understand scale factor from percentage

A 35% scale means the scale factor is 0.35 (since 35% = $\frac{35}{100}$ = 0.35).

Step2: Check similarity

Since both width and height are scaled by the same factor (0.35), the new image is similar to the original. The scale factor is 0.35 (or 35%).

Step1: Find scale factor for width

Divide new width by original width: $\frac{150}{300} = 0.5$.

Step2: Find scale factor for height

Divide new height by original height: $\frac{150}{450} = \frac{1}{3} \approx 0.333...$.

Step3: Determine similarity

Since the scale factors for width and height are different (0.5 vs. $\frac{1}{3}$), the new image is not similar to the original.

Answer:

a. The new image is similar to the original.
The original image was enlarged by a scale factor of 1.2.

Part b (New Image: 35% width, 35% height)