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 gj? what is the scale factor?

Explanation:

Step1: Identify corresponding sides

In similar figures, corresponding sides are in proportion. By observing the orientation and position of the sides in the two figures, we can see that $GJ$ corresponds to $BD$.

Step2: Calculate scale factor

Count the lengths of corresponding sides. Let the length of the side in the original figure ($GJ$) be 4 units and the length of the corresponding side in the scaled - copy ($BD$) be 2 units. Use the formula $k=\frac{\text{length of side in scaled copy}}{\text{length of side in original figure}}$. So $k=\frac{2}{4}=\frac{1}{2}$.

Answer:

1. The side in the figure on the right that corresponds to segment $GJ$ is $BD$.
2. The scale factor:

• First, count the vertical and horizontal lengths of corresponding sides. For example, if we consider the vertical side $GJ$, it has a length of 4 units (counting the grid - squares), and the corresponding vertical side $BD$ has a length of 2 units.
• The scale factor $k$ is found by the ratio of the lengths of corresponding sides of the scaled - copy to the original figure. Let the length of a side in the original figure be $l_1$ and the length of the corresponding side in the scaled copy be $l_2$. The scale factor $k=\frac{l_2}{l_1}$.
• Using the vertical sides $GJ$ and $BD$, we have $l_1 = 4$ (length of $GJ$) and $l_2=2$ (length of $BD$). So the scale factor $k = \frac{2}{4}=\frac{1}{2}$.