Question #15
Step-by-step explanation:
A notation such as [tex]T_{(-1, 1)}oR_{y-axis}[/tex] is read as:
"a translation of (x, y) → (x - 1, y + 1) after a reflection across y-axis.
- This process must be done from right to left
- Composition of transformations is not commutative
The rule of reflection of point (x, y) across y-axis brings (x, y) → (-x, y), meaning that y-coordinate remains the same, but x-coordinate changes its sign.
As ΔABC with coordinates A(1, 3), B(4, 5) and C(5, 2). Here is the coordinates of ΔA'B'C' after the glide reflection described by [tex]T_{(-1, 1)}oR_{y-axis}[/tex].
[tex]R_{y-axis}[/tex] [tex]T_{(-1, 1)}[/tex]
A(1, 3) → A'(-1, 3) → A"'(-2, 4)
B(4, 5) → B'(-4, 5) → B"'(-5, 6)
C(5, 2) → C'(-5, 2) → C"'(-6, 3)
Question #16
Step-by-step explanation:
A glide reflection is said to be a transformation that involves a translation followed by a reflection in which every point P is mapped to a point P ″ by the following steps.
- First, a translation maps P to P′.
- Then, a reflection in a line k parallel to the direction of the translation maps P′ to P ″.
As ΔABC with coordinates A(-4, -2), B(-2, 6) and C(4, 4).
Translation : (x, y) → (x + 2, y + 4)
Reflection : in the x-axis
The rule of reflection of point (x, y) across x-axis brings (x, y) → (x, -y), meaning that x-coordinate remains the same, but y-coordinate changes its sign.
Hence,
ΔABC with coordinates A(-4, -2), B(-2, 6), C(4, 4) after (x, y) → (x + 2, y + 4) and reflection in the x-axis.
A(-4, -2) → A'(-2, 2) → A''(-2, -2)
B(-2, 6) → B'(0, 10) → B''(0, -10)
C(4, 4) → C(6, 8) → C''(6, -8)
Keywords: reflection, glide reflection, translation
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