Question

a after the dilation. find the scale factor of the dilation. 11. a (-2, -3) and r (-10, -15) factor to write the ordered pairs after the dilation. 14. a(0, 0), b(-3, 2), and k = 5 2), and k = ¾

Explanation:

Step1: Recall dilation formula

For a dilation with scale - factor $k$, if a point $(x,y)$ is dilated, the new point $(x',y')$ is given by $(x',y')=(k\cdot x,k\cdot y)$. To find the scale - factor $k$ when given a pre - image point $(x_1,y_1)$ and an image point $(x_2,y_2)$, we use the formula $k=\frac{x_2}{x_1}=\frac{y_2}{y_1}$ (assuming $x_1
eq0$ and $y_1
eq0$).

Step2: Calculate scale factor for point A(-2,-3) and R(-10,-15)

For the $x$ - coordinates: $k=\frac{-10}{-2}=5$. For the $y$ - coordinates: $k = \frac{-15}{-3}=5$. So the scale factor of the dilation is $k = 5$.

Step3: Find the dilated points for A(0,0) and B(-3,2) with k = 5

For point A(0,0): Using the dilation formula $(x',y')=(k\cdot x,k\cdot y)$, when $x = 0$ and $y = 0$ and $k = 5$, we have $(x',y')=(5\times0,5\times0)=(0,0)$.
For point B(-3,2): When $x=-3$ and $y = 2$ and $k = 5$, we have $x'=k\cdot x=5\times(-3)=-15$ and $y'=k\cdot y=5\times2 = 10$. So the dilated point is (-15,10).

Answer:

For the scale - factor of the dilation of A(-2,-3) to R(-10,-15), the scale factor $k = 5$.
The dilated points for A(0,0) and B(-3,2) with $k = 5$ are A'(0,0) and B'(-15,10).