Question

for #7 - 9, dilate the figure that is graphed according to the given scale factor (k). 7. k = 2 8. k =.5 9. k = -1/2 10. what is the scale factor that created the dilation on the right? 11. what is the scale factor that created the dilation on the right?

Explanation:

Step1: Recall scale - factor formula

The scale factor $k$ of a dilation from a point $(x_1,y_1)$ to $(x_2,y_2)$ with the center of dilation at the origin is given by $k=\frac{x_2}{x_1}=\frac{y_2}{y_1}$ (assuming $x_1
eq0$ and $y_1
eq0$). We can also find the scale - factor by comparing the lengths of corresponding sides of the original and dilated figures.

Step2: For problem 10

Let's take a vertex of the original figure and its corresponding vertex of the dilated figure. For example, if we consider a vertex of the original square $ABCD$ and its corresponding vertex in the dilated square $A'B'C'D'$. Suppose a vertex of the original square is $(x_1,y_1)$ and the corresponding vertex of the dilated square is $(x_2,y_2)$. By counting the grid units, if we assume the center of dilation is the origin, we can see that the distance from the origin to a vertex of the dilated figure is half of the distance from the origin to the corresponding vertex of the original figure. So the scale factor $k = \frac{1}{2}$.

Step3: For problem 11

Similarly, for the dilation of the triangle $PQR$ to $P'Q'R'$, by comparing the lengths of corresponding sides (or the distances of corresponding vertices from the center of dilation, assumed to be the origin). If we take a side of the original triangle and its corresponding side in the dilated triangle, we find that the side - lengths of the dilated triangle are twice the side - lengths of the original triangle. So the scale factor $k = 2$.

Answer:

1. The scale factor is $\frac{1}{2}$.
2. The scale factor is $2$.