Question

part 2 of 2
the images on henrys digital camera have a width - to - length ratio of 2:3. he wants to make an 8 in. - by - 10 in. print of one of his photographs.
a. is this possible? explain.
b. how can henry crop an image so that an 8 in. - by - 10 in. print can be made?
b. how can henry crop the photo?
o a. he can enlarge it to 10 in. by 12 in. and then crop 2 in. from the width and 2 in. from the length.
o b. he can enlarge it to 8 in. by 12 in. and then crop 2 in. from the width.
o c. he can enlarge it to 8 in. by 12 in. and then crop 2 in. from the length.
o d. he can enlarge it to 10 in. by 10 in. and then crop 2 in. from the width.

Explanation:

Part a

Step1: Analyze the ratio

The width - to - length ratio of the camera is \(2:3\). For an \(8\) - by - \(10\) print, the ratio is \(8:10=\frac{8}{10}=\frac{4}{5}\). But if we consider the concept of dilation (scaling), we can adjust the image.
Let the width be \(2x\) and the length be \(3x\). We want to get a print with width \(w\) and length \(l\) such that \(w:l = 8:10\) (or an equivalent ratio after cropping). Since we can scale the image (enlarge or reduce) and then crop, it is possible.

Part b

Step1: Calculate the scaled dimensions

Let's assume we scale the image. If we scale the image by a factor. Suppose we first scale the image.
If we consider the length - based scaling:
Let the original width \(w = 2k\) and length \(l = 3k\).
If we want the length of the print to be \(10\) inches. Let \(3k\times m=10\) (where \(m\) is the scale factor). Then \(k=\frac{10}{3m}\). The width after scaling is \(2k\times m=\frac{20}{3}\approx6.67\) inches. Not helpful.
If we scale based on the width - to - length ratio of the print.
Let's assume we scale the image. Suppose we scale the image so that the width is \(12\) inches (a common scaling multiple). If the original ratio is \(2:3\), when width \(w = 12\) (scaled from \(2\) by a factor of \(6\)), the length \(l = 18\).
If we want an \(8\) - by - \(10\) print:
Option B:
If we first enlarge the width to \(8\) inches. Let the scale factor for width be \(s_w\). If the original width is \(2\) (from ratio \(2:3\)), and we want \(w = 8\), then \(s_w = 4\). The length becomes \(3\times4 = 12\). Then we crop \(2\) inches from the width (\(8\) inches (desired width) and we had a width of \(8\) (after scaling, assume we can adjust the region of the image) and crop \(2\) inches from the length (\(12-2 = 10\))

Answer:

a. Yes, it is possible. We can scale (enlarge or reduce) the image and then crop it to get the desired \(8\) - by - \(10\) print.
b. B. He can enlarge it to \(8\) in. by \(12\) in. and then crop \(2\) in. from the width.