Question

1. look at the values in the table. what do you the corresponding distance in the pause here so your teacher can review your work. 3. the larger figure is a scaled copy of the smaller figure. a) if ae = 4, how long is the corresponding distance in the second figure? explain or show your reasoning. 2 cause there correspondin distance in the example? b) if ik = 5, how long is the corresponding distance in the first figure? explain or show your reasoning.

Explanation:

Part (a)

Step1: Find the scale factor

From the figures, the length \( AB = 6 \) in the smaller figure corresponds to \( HI = 15 \) in the larger figure. The scale factor \( k \) from the smaller to the larger figure is \( k=\frac{15}{6}=\frac{5}{2} \).

Step2: Calculate the corresponding length

We know \( AE = 4 \) in the smaller figure. To find the corresponding length in the larger figure, we multiply \( AE \) by the scale factor \( k \). So the length \( = 4\times\frac{5}{2}=10 \).

Step1: Recall the scale factor

From part (a), the scale factor from the smaller to the larger figure is \( \frac{5}{2} \), so the scale factor from the larger to the smaller figure is the reciprocal, \( \frac{2}{5} \).

Step2: Calculate the corresponding length

We know \( IK = 5 \) in the larger figure. To find the corresponding length in the smaller figure, we multiply \( IK \) by the reciprocal scale factor. So the length \( = 5\times\frac{2}{5}=2 \).

Answer:

10

Part (b)