Ask a New Question
Menu

What is point

𝐴
A
(
6
,

7
)
(6, 7) after a translation of
4
4 units left and
5
5 units down followed by a 180° clockwise rotation around the origin

1 answer

To find the final position of point \( A(6, 7) \) after the specified transformations, follow the steps one by one.

  1. Translation:

    • Translating 4 units left subtracts 4 from the x-coordinate.
    • Translating 5 units down subtracts 5 from the y-coordinate.

    Starting point: \( A(6, 7) \)

    After translating 4 units left: \[ x' = 6 - 4 = 2 \] After translating 5 units down: \[ y' = 7 - 5 = 2 \]

    So, after the translation, point \( A \) becomes \( A'(2, 2) \).

  2. 180° Clockwise Rotation:

    • A 180° rotation around the origin transforms a point \( (x, y) \) to \( (-x, -y) \).

    For point \( A'(2, 2) \): \[ x'' = -2 \] \[ y'' = -2 \]

    So, after the rotation, point \( A' \) becomes \( A''(-2, -2) \).

Therefore, the final position of point \( A \) after the translation and rotation is \( (-2, -2) \).