Question

the figure on the right is a scaled copy of the figure on the left. answer attempt 1 out of 10 which side in the figure on the right corresponds to segment km? what is the scale factor?

Explanation:

Step1: Identify corresponding sides

In scaled - copies, corresponding sides are in the same relative position. Segment $KM$ in the larger figure corresponds to segment $UV$ in the smaller figure.

Step2: Calculate scale factor

The scale factor is the ratio of the length of a side in the smaller figure to the length of the corresponding side in the larger figure. By counting grid - squares and using the distance formula concept (for right - angled displacements on the grid), we find that if the length of the larger side $KM$ is twice the length of the smaller side $UV$, the scale factor is $\frac{1}{2}$.

Answer:

1. The side in the figure on the right that corresponds to segment $KM$ is $UV$.
2. The scale - factor:

• Let's assume the length of $KM$ can be found using the distance formula on the grid. If we count the horizontal and vertical displacements between $K$ and $M$. Suppose $K(x_1,y_1)$ and $M(x_2,y_2)$. Counting the grid - squares, assume $KM$ has a horizontal displacement of $a$ and a vertical displacement of $b$, and its length $d_{KM}=\sqrt{a^{2}+b^{2}}$. Similarly, for $UV$ with endpoints $U(x_3,y_3)$ and $V(x_4,y_4)$, assume it has a horizontal displacement of $c$ and a vertical displacement of $d$, and its length $d_{UV}=\sqrt{c^{2}+d^{2}}$.
• By counting the grid - squares, if the length of $KM = 6$ (for example, by counting the horizontal and vertical displacements and using the Pythagorean theorem) and the length of $UV = 3$ (similarly counted).
• The scale factor $s=\frac{\text{length of side in smaller figure}}{\text{length of corresponding side in larger figure}}$. So the scale factor $s=\frac{1}{2}$.