Transformations (Copy)
Q1 (Non-Calculator)
Reflect the point (3, 2) in the line x = 0 (the y-axis). Find the coordinates of the image.
Solution:
Reflection over the y-axis changes (x, y) → (–x, y).
Image = (–3, 2)
Answer:
(–3, 2)
Q2 (Non-Calculator)
Reflect the point (–4, 1) in the line y = 0 (the x-axis). Find the coordinates of the image.
Solution:
Reflection over the x-axis changes (x, y) → (x, –y).
Image = (–4, –1)
Answer:
(–4, –1)
Q3 (Non-Calculator)
Rotate the point (2, 5) 90° anticlockwise about the origin. Find the coordinates of the image.
Solution:
90° anticlockwise rotation: (x, y) → (–y, x).
Image = (–5, 2)
Answer:
(–5, 2)
Q4 (Non-Calculator)
Rotate the point (–3, 1) 180° about the origin. Find the coordinates of the image.
Solution:
180° rotation: (x, y) → (–x, –y).
Image = (3, –1)
Answer:
(3, –1)
Q5 (Non-Calculator)
Rotate the point (4, –2) 270° anticlockwise about the origin. Find the coordinates of the image.
Solution:
270° anticlockwise rotation: (x, y) → (y, –x).
Image = (–2, –4)
Answer:
(–2, –4)
Q6 (Calculator)
Enlarge the point (2, 3) from the origin with scale factor 2. Find the coordinates of the image.
Solution:
Multiply each coordinate by 2:
(2×2, 3×2) = (4, 6)
Answer:
(4, 6)
Q7 (Calculator)
Enlarge the point (6, –4) from the origin with scale factor 0.5. Find the coordinates of the image.
Solution:
Multiply each coordinate by 0.5:
(6×0.5, –4×0.5) = (3, –2)
Answer:
(3, –2)
Q8 (Calculator)
Translate the point (–2, 5) by the vector
(3−2)begin{pmatrix} 3 \ -2 end{pmatrix}
Find the coordinates of the image.
Solution:
Move 3 right and 2 down:
(–2 + 3, 5 – 2) = (1, 3)
Answer:
(1, 3)
Q9 (Calculator)
Translate the point (1, –1) by the vector
(−46)begin{pmatrix} -4 \ 6 end{pmatrix}
Find the coordinates of the image.
Solution:
Move 4 left and 6 up:
(1 – 4, –1 + 6) = (–3, 5)
Answer:
(–3, 5)
Q10 (Calculator)
An enlargement of scale factor 3 from the origin maps the point (–2, 1) to what new coordinates?
Solution:
Multiply each coordinate by 3:
(–2×3, 1×3) = (–6, 3)
Answer:
(–6, 3)