Question

Quadrilateral ABCD is shown.

-5
A
3
N
6
2
5-
3-
2-
1-
10
-1-
-24
-3-
-4-
-5-
A
B
(a) Work out the coordinates of C when ABCD is
Rotated 900 clockwise about 0
then
translated by
1 2
3
D
с
4
5
[2 marks]

Answer 1

C'(-5, -2)

Explanation:

You want the coordinates of point C(4, 1) after rotation 90° CW about the origin and translation by (-6, 2).

Rotation

The transformation accomplished by rotation 90° clockwise is ...

(x, y) ⇒ (y, -x)

Translation

The translation by (-6, 2) adds those values to the coordinates:

(x, y) ⇒ (x -6, y +2)

Both transformations

Combined, the transformations give you ...

(x, y) ⇒ (y -6, -x +2)

C(4, 1) ⇒ C'(1 -6, -4 +2) = C'(-5, -2)

The coordinates of C after the transformation(s) are (-5, -2).