Answer:
Option B is correct.
Rule of dilation of the figure STUV is: [tex](x, y) \rightarrow (0.2x , 0.2y)[/tex]
Step-by-step explanation:
From the given figure;
the coordinates of STUV pre -image are;
S = (-5 , -5) ,
T = (5, -5)
U = (10 , 5)
V = (-10 , 5)
And the coordinates of dilated image S'T'U'V' are;
S' = (-1, -1)
T' = (1, -1)
U' = (2, 1)
V' = (-2, 1)
The rule of dilation with scale factor k centered at the origin is given by:
[tex](x, y) \rightarrow (kx , ky)[/tex]
To solve for k;
Let any pre-image S(x, y)= (-5, -5)
here, x = -5 and y = -5
then;
S'(kx, ky) = (-1, -1)
Substitute value of x and y we get;
(-5k , -5k) = (-1, -1)
On comparing both sides we get;
-5 k = -1
Divide both sides by -5 we get;
[tex]k= \frac{-1}{-5} = \frac{1}{5} = 0.2[/tex]
Therefore, the rule which yields the dilation of the figure STUV centered at the origin is; [tex](x, y) \rightarrow (0.2x , 0.2y)[/tex]
