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3 years ago

PLEASE HELP! find (1,2) obtained by translating 2 units down followed by a rotation of 180 counterclockwise.

Mathematics

1 answer:

N76 [4]3 years ago

6 0

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

P(1, 2)

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

P(2, 4)

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)

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