Question

preimage
image
scale factor × 10
what is the area of the preimage?
○ 600 units²
○ 6 units²
○ \\(\frac{6}{10}\\) units²
○ 60 units²

Explanation:

Step1: Find area of image

The image is a right triangle with legs 40 and 30. The area of a right triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. So, area of image is $\frac{1}{2} \times 30 \times 40 = 600$ square units.

Step2: Relate preimage and image areas

When a figure is scaled by a scale factor \( k \), the area of the image is \( k^2 \) times the area of the preimage. Here, scale factor \( k = 10 \), so area of image \( = 10^2 \times \) area of preimage. Let \( A \) be the area of preimage. Then \( 600 = 100 \times A \).

Step3: Solve for preimage area

To find \( A \), divide both sides by 100: \( A=\frac{600}{100} = 6 \) square units.

Answer:

6 units²