Transformations (Copy)

1.

Reflect triangle A(2,3), B(4,3), C(3,6) in the line x=0. Write down the coordinates of the image.

2.

Reflect the same triangle (from Q1) in the line y=0.

3.

Rotate triangle P(1,2), Q(3,2), R(2,4) 90° anticlockwise about the origin. Give the new coordinates.

4.

Rotate triangle PQR (from Q3) 180° about the origin.

5.

Enlarge triangle X(2,1), Y(4,1), Z(3,3) by scale factor 2 about the origin.

6.

Enlarge the same triangle (from Q5) by scale factor −1 about the origin.

7.

Translate square A(1,1), B(3,1), C(3,3), D(1,3) by vector (4, −2).

8.

Translate triangle J(−2,0), K(−1,3), L(−3,2) by vector (−3, 5).

9.

Reflect quadrilateral A(0,0), B(2,0), C(2,2), D(0,2) in the line y=x.

10.

Rotate the same quadrilateral (from Q9) 270° clockwise about the origin.

11.

A triangle is reflected in the line x=2, then rotated 180° about the origin. Describe the single transformation.

12.

A square is translated by (2,−3) then reflected in y=0. Write the matrix/vector form of the combined transformation.

13.

Enlarge triangle A(0,0), B(2,0), C(1,2) by scale factor 3, centre (0,0). Find the new coordinates.

14.

Enlarge the same triangle (from Q13) by scale factor ½, centre (0,0).

15.

A shape is enlarged by scale factor −2 about the origin. State the effect on orientation and size.

16.

Reflect A(2,5) in y=3. Give the image coordinates.

17.

Reflect A(−4,−2) in the line x=−1.

18.

Rotate point P(5,0) 90° anticlockwise about the origin.

19.

Rotate point Q(0,−7) 270° anticlockwise about the origin.

20.

Translate point R(−3,4) by vector (6,−2).

21.

Find the image of triangle A(1,0), B(0,2), C(2,3) under reflection in y=−x.

22.

Find the coordinates of triangle A(2,2), B(4,2), C(3,5) after rotation 90° clockwise about (0,0).

23.

A quadrilateral has vertices A(−2,−1), B(−4,−1), C(−4,−3), D(−2,−3).
Translate it by (3,4).

24.

Reflect the quadrilateral (from Q23) in x=0.

25.

A shape has vertices A(1,1), B(2,1), C(2,2), D(1,2). It is enlarged by scale factor 3 about (1,1). Find the coordinates.

26.

Enlarge triangle A(0,1), B(2,1), C(1,3) by scale factor −½ about the origin.

27.

Describe fully the transformation that maps (x,y) → (−y,x).

28.

Describe fully the transformation that maps (x,y) → (−x,−y).

29.

A triangle is rotated 180° about the origin, then reflected in y=0. Describe the single transformation.

30.

A rectangle has vertices (0,0), (6,0), (6,2), (0,2). It is enlarged by scale factor 2 about the origin, then translated by (−3,4). Find final coordinates.

1.
Reflection in x=0 (y-axis) changes (x,y) → (−x,y).
A(2,3)→(−2,3), B(4,3)→(−4,3), C(3,6)→(−3,6).

2.
Reflection in y=0 (x-axis) changes (x,y) → (x,−y).
A(2,3)→(2,−3), B(4,3)→(4,−3), C(3,6)→(3,−6).

3.
Rotation 90° anticlockwise about origin: (x,y) → (−y,x).
P(1,2)→(−2,1), Q(3,2)→(−2,3), R(2,4)→(−4,2).

4.
Rotation 180° about origin: (x,y) → (−x,−y).
P(1,2)→(−1,−2), Q(3,2)→(−3,−2), R(2,4)→(−2,−4).

5.
Enlargement SF=2, centre (0,0): multiply coordinates by 2.
X(2,1)→(4,2), Y(4,1)→(8,2), Z(3,3)→(6,6).

6.
Enlargement SF=−1: multiply coordinates by −1.
X(2,1)→(−2,−1), Y(4,1)→(−4,−1), Z(3,3)→(−3,−3).
Orientation is reversed.

7.
Translation (4,−2): add vector.
A(1,1)→(5,−1), B(3,1)→(7,−1), C(3,3)→(7,1), D(1,3)→(5,1).

8.
Translation (−3,5).
J(−2,0)→(−5,5), K(−1,3)→(−4,8), L(−3,2)→(−6,7).

9.
Reflection y=x: (x,y) → (y,x).
A(0,0)→(0,0), B(2,0)→(0,2), C(2,2)→(2,2), D(0,2)→(2,0).

10.
Rotation 270° clockwise ≡ 90° anticlockwise: (x,y)→(−y,x).
A(0,0)→(0,0), B(2,0)→(0,2), C(2,2)→(−2,2), D(0,2)→(−2,0).

11.
Reflection in x=2 then 180° rotation about origin → overall is reflection in line x=−2.

12.
Translation (2,−3) then reflection in y=0: (x,y)→(x+2,−y+3).

13.
Enlargement SF=3 about (0,0): multiply by 3.
A(0,0)→(0,0), B(2,0)→(6,0), C(1,2)→(3,6).

14.
Enlargement SF=½: multiply by 0.5.
A(0,0), B(2,0)→(1,0), C(1,2)→(0.5,1).

15.
Enlargement SF=−2: size ×2, orientation reversed (flipped through origin).

16.
Reflection y=3: image distance same above/below.
Point (2,5): difference=2 → image= (2,1).

17.
Reflection x=−1: difference from −1 = (−4)−(−1)=−3. Image at (1,−2).

18.
Rotation 90° anticlockwise: (x,y)→(−y,x).
(5,0)→(0,5).

19.
Rotation 270° anticlockwise: (x,y)→(y,−x).
(0,−7)→(−7,0).

20.
Translate (−3,4) by (6,−2) → (−3+6,4−2)=(3,2).

21.
Reflection in y=−x: (x,y)→(−y,−x).
A(1,0)→(0,−1), B(0,2)→(−2,0), C(2,3)→(−3,−2).

22.
Rotation 90° clockwise: (x,y)→(y,−x).
A(2,2)→(2,−2), B(4,2)→(2,−4), C(3,5)→(5,−3).

23.
Translation (3,4).
A(−2,−1)→(1,3), B(−4,−1)→(−1,3), C(−4,−3)→(−1,1), D(−2,−3)→(1,1).

24.
Reflect in x=0: change (x,y)→(−x,y).
A(1,3)→(−1,3), B(−1,3)→(1,3), etc. (apply accordingly).

25.
Scale factor 3, centre (1,1): new coords (x′,y′)=(1+3(x−1), 1+3(y−1)).
A(1,1)→(1,1), B(2,1)→(4,1), C(2,2)→(4,4), D(1,2)→(1,4).

26.
SF=−½ about origin. Multiply by −0.5.
A(0,1)→(0,−0.5), B(2,1)→(−1,−0.5), C(1,3)→(−0.5,−1.5).

27.
Mapping (x,y)→(−y,x) is a rotation 90° anticlockwise about the origin.

28.
Mapping (x,y)→(−x,−y) is a rotation 180° about the origin.

29.
Rotation 180° then reflection y=0 is same as reflection in y=0 followed by rotation 180°.
Equivalent single transformation: reflection in x=0.

30.
First enlargement SF=2: multiply coords by 2.
(0,0),(12,0),(12,4),(0,4).
Then translation (−3,4): subtract 3 from x, add 4 to y.
(−3,4),(9,4),(9,8),(−3,8).