Question 1)
Answer:
Please see the explanation.
Step-by-step explanation:
We know that the dilation of an original object shows how much bigger or smaller the image will really get, as compared to the original shape.
Also,
- if the value of scale factor > 1, the image will get bigger.
- if the value of scale factor < 1, the image will get smaller.
The new coordinates of the image can be determined by multiplying the scale factor with the coordinates of the original object.
Given the preimage points:
The formula of the dilation by a scale factor of 3:
(x, y) → (3x, 3y)
- As the scale factor > 1, so the image will be bigger.
Therefore, the coordinates of the dilated image after the dilation by a scale factor of 3 will be:
A(x, y) → (3x, 3y) = A(0, 5) → (3(0), 3(5)) = A'(0, 15)
B(x, y) → (3x, 3y) = B(4, 9) → (3(4), 3(9)) = B'(12, 27)
C(x, y) → (3x, 3y) = C(-1, -8) → (3(-1), 3(-8)) = C'(-3, -24)
Question 2)
Answer:
Please see the explanation.
Step-by-step explanation:
Given the preimage points:
The formula of the dilation by a scale factor of 1/2:
(x, y) → (1/2x, 1/2y)
- As the scale factor < 1, so the image will be smaller.
Therefore, the coordinates of the dilated image after the dilation by a scale factor of 1/2 will be:
A(x, y) → (3x, 3y) = A(0, 5) → (1/2(0), 1/2(5)) = A'(0, 5/2)
B(x, y) → (3x, 3y) = B(4, 9) → (1/2(4), 1/2(9)) = B'(2, 9/2)
C(x, y) → (3x, 3y) = C(-1, -8) → (1/2(-1), 1/2(-8)) = C'(-1/2, -4)
