Answer:
Please check the explanation.
Step-by-step explanation:
Translating two units down means we need to subtract two units from the y-coordinate. i.e
(x, y) → (x, y-2)
We are given that the original point is (1, 2), and we have to find the image of (2, 4) obtained by translating 2 units down followed by a rotation of 180 counterclockwise.
FOR (1, 2)
Given
First translation: Translating two units down
(x, y) → (x, y-2)
P(1, 2) → P'(1, 2-2) → P'(1, 0)
Second transformation: Rotation of 180 counterclockwise.
Rotation of 180 counterclockwise will make both 'x' and 'y' coordinates negative. i.e
(x, y) → (-x, -y)
Thus, after second transformation
P'(1, 0) → (-1, 0)
Thus, the image of (1, 2) obtained by translating 2 units down followed by a rotation of 180 counterclockwise will be: (-1, 0)
FOR (2, 4)
Given
First translation: Translating two units down
(x, y) → (x, y-2)
P(2, 4) → P'(2, 4-2) → P'(2, 2)
Second transformation: Rotation of 180 counterclockwise.
Rotation of 180 counterclockwise will make both 'x' and 'y' coordinates negative. i.e
(x, y) → (-x, -y)
Thus, after the second transformation
P'(2, 2) → (-2, -2)
Thus, the image of (2, 4) obtained by translating 2 units down followed by a rotation of 180 counterclockwise will be: (-2, -2)
