. Describe the sequence of
transformations from ΔA to ΔB.
B. reflection over
the x-axis and
translation a
2 units down.
C. 90° rotation
counterclockwise
and a translation
1 unit right.
D. reflection over
the y-axis and a
translation 2 units
down.
B. The sequence of transformations from ΔA to ΔB is a reflection over the x-axis followed by a translation 2 units down.
C. The sequence of transformations from ΔA to ΔB is a 90° counter-clockwise rotation followed by a translation 1 unit to the right.
D. The sequence of transformations from ΔA to ΔB is a reflection over the y-axis followed by a translation 2 units down.
which one
The correct answer is:
B. The sequence of transformations from ΔA to ΔB is a reflection over the x-axis followed by a translation 2 units down.
show work
To visually understand the sequence of transformations from ΔA to ΔB, let's draw the triangles on a coordinate grid.
Let's say that the vertices of ΔA are A(1, 3), B(4, 6), and C(7, 3).
1. Reflection over the x-axis:
To reflect the triangle over the x-axis, we need to change the sign of the y-coordinate of each point.
The new coordinates of the vertices after reflection are A(1, -3), B(4, -6), and C(7, -3).
2. Translation 2 units down:
To translate the triangle 2 units down, we subtract 2 from the y-coordinate of each point.
The new coordinates of the vertices after translation are A(1, -5), B(4, -8), and C(7, -5).
Now, let's visualize the transformation:
Before reflection and translation: ΔA with vertices A(1, 3), B(4, 6), and C(7, 3)
After reflection over the x-axis: ΔA' with vertices A'(1, -3), B'(4, -6), and C'(7, -3)
After translation 2 units down: ΔB with vertices A(1, -5), B(4, -8), and C(7, -5)
Therefore, the sequence of transformations from ΔA to ΔB is a reflection over the x-axis followed by a translation 2 units down.