The dilation D: (x, y) → (0.2x, 0.2y) has been applied to the polygon S(–5, 5), T(–5, 10), U(5, 15). What are the coordinates of the image points?
a
S'(–1, 1), T'(–1, 2), U'(1, 3)
b
S'(–4.8, 5.2), T'(–4.8, 10.2), U'(5.2, 15.2)
c
S'(–5.2, 4.8), T'(–5.2, 9.8), U'(4.8,14.8)
d
S'(–3, 7), T'(–3, 12), U'(7, 17)
S(-5,5) -> S'(-5*0.2,5*0.2) = (-1,1)
and so on
To find the image points after applying the dilation D: (x, y) → (0.2x, 0.2y), we need to multiply the x and y coordinates of each point by 0.2.
Applying the dilation to S(–5, 5):
S'(0.2*(-5), 0.2*5)
S'(-1, 1)
Applying the dilation to T(–5, 10):
T'(0.2*(-5), 0.2*10)
T'(-1, 2)
Applying the dilation to U(5, 15):
U'(0.2*5, 0.2*15)
U'(1, 3)
Therefore, the coordinates of the image points are:
S'(–1, 1), T'(–1, 2), U'(1, 3)
So the correct answer is option (a):
S'(–1, 1), T'(–1, 2), U'(1, 3)
To find the image points after the dilation D: (x, y) → (0.2x, 0.2y), we need to multiply the coordinates of each point of the original polygon by a scale factor of 0.2.
Let's calculate the image points for each of the given points:
For S(-5, 5):
S' = (0.2 * -5, 0.2 * 5) = (-1, 1)
For T(-5, 10):
T' = (0.2 * -5, 0.2 * 10) = (-1, 2)
For U(5, 15):
U' = (0.2 * 5, 0.2 * 15) = (1, 3)
Now, let's compare the calculated image points with the answer choices:
a) S'(-1, 1), T'(-1, 2), U'(1, 3)
b) S'(-4.8, 5.2), T'(-4.8, 10.2), U'(5.2, 15.2)
c) S'(-5.2, 4.8), T'(-5.2, 9.8), U'(4.8, 14.8)
d) S'(-3, 7), T'(-3, 12), U'(7, 17)
From the calculations, we see that the answer is option a. So, the correct coordinates of the image points are:
S'(–1, 1), T'(–1, 2), U'(1, 3)