Question

problem 9 tayen says that figure k is a scaled copy of figure g. is tayen correct? yes no explain your thinking.

Explanation:

Step1: Check scale factor

To determine if Figure K is a scaled copy of Figure G, we check the ratio of corresponding side lengths. For a scaled copy, all corresponding linear dimensions should have the same scale factor.
Looking at the vertical side of Figure G (let's assume the vertical segment of the "notch" or the overall height - related part) and Figure K. Wait, actually, looking at the given dimensions: Figure G has a vertical segment (let's say the height of the main part or the width of the notch - related) as 4 cm, and Figure K has 2 cm. Wait, no, maybe the horizontal or vertical? Wait, actually, in a scaled copy, the ratio of all corresponding lengths should be equal. Let's check the width of the "arms" or the notches. Wait, maybe the key is the scale factor. Let's see: if Figure G has a side of 4 cm and Figure K has 2 cm, the scale factor would be \( \frac{2}{4}=\frac{1}{2} \). Now, we need to check if all corresponding sides are scaled by \( \frac{1}{2} \). If the shape of Figure K is a reduction (or enlargement) of Figure G with the same scale factor for all sides, then it's a scaled copy. Wait, but maybe the original problem's figures: Figure G and Figure K. Let's assume that the linear dimensions of Figure K are half of Figure G (since 2 is half of 4). So if all sides of K are \( \frac{1}{2} \) of G, then it's a scaled copy. So Tayen is correct? Wait, no, wait. Wait, maybe I misread. Wait, the problem: Is Figure K a scaled copy of Figure G? Let's think about scaled copies: a scaled copy is a resizing (enlargement or reduction) of the original figure by a scale factor, where all angles remain the same and all side lengths are multiplied by the same scale factor. So if Figure G has a side length of 4 cm (say, the height of the "notch" part or the width of the main body) and Figure K has 2 cm, then the scale factor is \( \frac{2}{4} = \frac{1}{2} \). If all other corresponding sides are also scaled by \( \frac{1}{2} \), then it's a scaled copy. So Tayen is correct? Wait, but maybe the figures: let's see, Figure G and Figure K. If Figure G's vertical segment (the height of the "U - like" part) is 4 cm, and Figure K's is 2 cm, and the horizontal segments (the width of the notches, the length of the arms) are also scaled by \( \frac{1}{2} \), then yes, it's a scaled copy. So the answer would be Yes, because the scale factor between corresponding sides is constant (2/4 = 1/2, so all sides of K are 1/2 of G, preserving the shape, so it's a scaled copy.

Wait, but maybe I made a mistake. Wait, let's re - examine. A scaled copy must have all corresponding linear measurements in proportion. So if Figure G has a side of length \( l_G \) and Figure K has \( l_K \), then \( \frac{l_K}{l_G} \) should be the same for all corresponding sides. If in Figure G, a certain side is 4 cm, and in Figure K, the corresponding side is 2 cm, then the scale factor is \( \frac{2}{4}=\frac{1}{2} \). If other sides also follow this ratio, then it's a scaled copy. So Tayen is correct.

Answer:

Yes, because the ratio of corresponding side lengths (e.g., 2 cm in K to 4 cm in G) is constant (\( \frac{1}{2} \)), meaning all sides of K are scaled by the same factor from G, so K is a scaled copy of G.