Answer:
Step-by-step explanation:
Coordinates of the vertices of the given rectangle are,
A(-4, 5), B(-2, 5), C(-2,1) and D(-4, 1).
If the given rectangle ABCD is translated by 1 unit right and 4 units down,
Rule for the translation will be,
(x, y) → [(x + 1), (y - 4)]
Therefore, coordinates of A, B, C and D after translation will be,
A(-4, 5) → A'(-3, 1)
B(-2, 5) → B'(-1, 1)
C(-2, 1) → C'(-1, -3)
D(-4, 1) → D'(-3, -3)
Then A', B', C' and D' are reflected about the y-axis.
Rule for the reflection about y-axis will be,
(x, y) → (-x, y)
New coordinates after the reflection will be,
A'(-3, 1) → A"(3, 1)
B'(-1, 1) → B"(1, 1)
C'(-1, -3) → C"(1, -3)
D'(-3, -3) → D''(3, -3)
Finally these points are rotated 270° clockwise about the origin,
Rule to be followed,
(x, y) → (-y, x)
Therefore, new coordinates will be,
A"(3, 1) → A"'(-1, 3)
B"(1, 1) → B'"(-1, 1)
C"(1, -3) → C"'(3, 1)
D"(3, -3) → D"'(3, 3)
