Question

On a computer screen, lengths and widths are measured not in inches or millimeters but

in pixels. A pixel is the smallest visual element that a computer is capable of processing. A
common size for a large computer screen is 1024 × 768 pixels. (Widths rather than heights are
conventionally listed first.) For the following, assume you’re working on a 1024 × 768 screen.
1. You have a photo measuring 640 × 300 pixels and you
want to enlarge it proportionally so that it is as wide as the
computer screen. Find the measurements of the photo after it
has been scaled up. Explain how you found the answer.
2. a. Explain why you can’t enlarge the photo proportionally so
that it is as tall as the computer screen.
b. Why can’t you correct the difficulty in (a) by scaling the
width of the photo by a factor of 1024 ÷ 640 and the
height by a factor of 768 ÷ 300

Answer 1

To enlarge the photo proportionally, we need to scale it up by the same factor in both dimensions. Since we want to scale it so that its width matches the width of the screen, we can find the scaling factor by dividing the screen width by the photo width:

scaling factor = screen width / photo width = 1024 / 640 = 1.6

Now we can use this scaling factor to find the new height of the photo:

new height = photo height x scaling factor = 300 x 1.6 = 480 pixels

Therefore, after the photo is scaled up proportionally, its measurements are 1024 x 480 pixels.

2a. We can't enlarge the photo proportionally so that it is as tall as the computer screen because its aspect ratio (the ratio of its width to its height) is different from the aspect ratio of the screen. The photo's aspect ratio is 640/300 = 2.13, while the screen's aspect ratio is 1024/768 = 1.33. Enlarging the photo so that its height matches the screen's height would require stretching the photo vertically, which would distort the image.

2b. Scaling the width of the photo by a factor of 1024/640 and the height by a factor of 768/300 would not correct the difficulty in part (a) because it would not change the aspect ratio of the photo. The aspect ratio of the photo would still be 2.13, which is different from the aspect ratio of the screen. The photo would still need to be stretched vertically to match the screen's height, which would distort the image.

Answer 2

To enlarge the photo proportionally so that it is as wide as the computer screen, we need to find the scaling factor. The scaling factor is the ratio of the width of the computer screen to the width of the photo:

Scaling factor = 1024 ÷ 640 = 1.6

We can then use this scaling factor to find the new dimensions of the photo:

New width = 640 × 1.6 = 1024 pixels

New height = 300 × 1.6 = 480 pixels

Therefore, the new dimensions of the photo are 1024 × 480 pixels.

2a. We cannot enlarge the photo proportionally so that it is as tall as the computer screen because the aspect ratio of the photo is different from the aspect ratio of the computer screen. The aspect ratio of the photo is 640 ÷ 300 ≈ 2.13, while the aspect ratio of the computer screen is 1024 ÷ 768 ≈ 1.33. This means that if we enlarge the height of the photo to match the height of the computer screen, the width of the photo will be too wide to fit on the screen.

b. We cannot correct the difficulty in (a) by scaling the width of the photo by a factor of 1024 ÷ 640 and the height by a factor of 768 ÷ 300 because this would change the aspect ratio of the photo. The aspect ratio of the photo would become 1024 ÷ (640 × 1024 ÷ 640) ≈ 1.6, which is the same as the aspect ratio of the computer screen. However, the height of the photo would be scaled by a factor of 768 ÷ 300 ≈ 2.56, which would make the photo too tall to fit on the screen.