Li is a professional nature photographer. She takes photograph of a spider web and prints a copy. Da original of her copy are 6 inches by 4 inches LI decides to advertise her business by printing smaller copies of da spider web photograph and emailing them to friends and acquaintances. Which dimensions represent a smaller scale drawing of da original printed photograph?

Question

1.5 inches by 1 inch

12 inches by 8 inches

2 inches by 1 inch

1 inch by 0.5 inches

Answer 1

To find which dimensions represent a smaller scale drawing of the original photograph (6 inches by 4 inches), we need to ensure that the aspect ratio (the proportional relationship between the width and height) remains the same while also being smaller than the original size.

The aspect ratio of the original photograph is:

\[ \text{Aspect Ratio} = \frac{6}{4} = \frac{3}{2} \]

Now, let's check the dimension options provided to see which ones maintain that aspect ratio and are smaller than the original dimensions:

1. 1.5 inches by 1 inch: \[ \text{Aspect Ratio} = \frac{1.5}{1} = 1.5 \quad \text{(which is } \frac{3}{2}) \] This option maintains the aspect ratio and is smaller.

2. 12 inches by 8 inches: \[ \text{Aspect Ratio} = \frac{12}{8} = 1.5 \quad \text{(which is } \frac{3}{2}) \] This option maintains the aspect ratio but is larger than the original dimensions.

3. 2 inches by 1 inch: \[ \text{Aspect Ratio} = \frac{2}{1} = 2 \] This does not match the original aspect ratio.

4. 1 inch by 0.5 inches: \[ \text{Aspect Ratio} = \frac{1}{0.5} = 2 \] This does not match the original aspect ratio.

The only dimensions that represent a smaller scale drawing of the original photograph while maintaining the same aspect ratio are:

1.5 inches by 1 inch.