Question

1. point r is the image of a after the dilation. find the scale factor of the dilation.
2. a (9, 12) and r (6, 8)
3. a (-2, -3) and r (-10, -15)

endpoints. use the scale factor to write the ordered pairs after the dilation.

1. a(4,4 ), b(8, 12), and k = 3/4
2. a(0, 0), b(-3, 2), and k = 5

Explanation:

Step1: Recall dilation formula

For a dilation centered at the origin, if a point $A(x_1,y_1)$ is dilated to $R(x_2,y_2)$, the scale - factor $k=\frac{x_2}{x_1}=\frac{y_2}{y_1}$.

Step2: Solve for problem 10

Given $A(9,12)$ and $R(6,8)$. Calculate $k$ using the $x$ - coordinates: $k=\frac{6}{9}=\frac{2}{3}$. Calculate $k$ using the $y$ - coordinates: $k = \frac{8}{12}=\frac{2}{3}$.

Step3: Solve for problem 11

Given $A(-2,-3)$ and $R(-10,-15)$. Calculate $k$ using the $x$ - coordinates: $k=\frac{-10}{-2}=5$. Calculate $k$ using the $y$ - coordinates: $k=\frac{-15}{-3}=5$.

Step4: Solve for problem 13

Given $A(4,4)$, $B(8,12)$ and $k = \frac{3}{4}$. For point $A$, the new coordinates $A'(x,y)$: $x=4\times\frac{3}{4}=3$, $y = 4\times\frac{3}{4}=3$, so $A'(3,3)$. For point $B$, the new coordinates $B'(x,y)$: $x=8\times\frac{3}{4}=6$, $y=12\times\frac{3}{4}=9$, so $B'(6,9)$.

Step5: Solve for problem 14

Given $A(0,0)$, $B(-3,2)$ and $k = 5$. For point $A$, the new coordinates $A'(x,y)$: $x=0\times5 = 0$, $y=0\times5=0$, so $A'(0,0)$. For point $B$, the new coordinates $B'(x,y)$: $x=-3\times5=-15$, $y=2\times5 = 10$, so $B'(-15,10)$.

Answer:

1. $k=\frac{2}{3}$
2. $k = 5$
3. $A'(3,3)$, $B'(6,9)$
4. $A'(0,0)$, $B'(-15,10)$