Reflections
Point B(–6, 3) is reflected across the line y = x. What are the coordinates of its image?
(3, –6)
Point Q(–4, –3) is translated by vector ⟨2, –5⟩. What is its image?
(–2, –8)
After reflecting D(3,–5) across the x-axis, then translating ⟨–4, 6⟩, where is the image?
(–1, 11)
A dilation multiplies each coordinate by a constant. What is that constant called?
The scale factor
Reflection over y = x swaps which coordinates?
x and y
Point D(3, –5) is reflected across the x-axis. What are its new coordinates?
(3, 5)
The translation rule (x, y) → (x +5, y + 4). How does this affect the coordinates?
Moves 5 right and 4 up
Which quadrant is (–1, 11) located in?
Quadrant II
Triangle 1 → Triangle 2: each coordinate multiplied by ½. What type of transformation?
Dilation, scale factor ½
A matrix rule (x, y) → (–x, –y) represents what?
180° rotation about the origin
A point (4, –2) is reflected across the y-axis. What is its image?
(–4, –2)
The translation vector ⟨–3, 6⟩ moves a shape how?
3 units left, 6 units up
Translation is the composition of what two reflections?
Two reflections over parallel lines
How are the side lengths related if the scale factor is ⅓?
Each side is one-third as long
If only the x-row of a matrix is negated, what reflection occurred?
Reflection over the y-axis
Reflection across the line y = –x changes a point (x, y) to what rule?
(–y, –x)
Segment midpoint is (4,3) and one endpoint is (1,2). Find the other endpoint.
(7,4)
What happens to slopes of corresponding sides after a translation?
Slopes remain equal (lines stay parallel)
A figure is dilated by a scale factor of 2 with the center at the origin. How do the coordinates of each vertex change?
Each coordinate is multiplied by 2(x′ = 2x, y′ = 2y)
The matrix rule (x, y) → (y, x) represents what reflection?
Reflection over y = x
A triangle with vertices (1,2), (3,5), and (4,1) is reflected across y = x. List the coordinates of its image.
(2,1), (5,3), (1,4)
What translation vector takes (–3,4) to (5, –2)?
⟨8, –6⟩
After reflecting across y-axis then x-axis, what ordered pair rule results?
(x, y) → (–x, –y)
A triangle is dilated with a scale factor of 3 about the origin. One vertex is at (–2, 4). What are the coordinates of its image?
(–6, 12)
How do you find the translation vector between two coordinate matrices?
Subtract original coordinates from image coordinates: ⟨x'–x, y'–y⟩