Question

Quadrilateral ABCD undergoes a reflection across the x-axis to form quadrilateral A'B'C'D'. The coordinates of A' are (
,
).

The reflected quadrilateral A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D". The coordinates of A" are (
,
).

Answer 1

Answer:

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Answer 2

Given:

Quadrilateral ABCD undergoes reflection across x-axis to form quadrilateral A'B'C'D'.

A'B'C'D' is then translated 3 units right and 2 units up to form quadrilateral A"B"C"D"

To find:

Coordinates of A' and A"

Solution:

Let point A have coordinates $(x_{1},y_{1})$, point B have coordinates $(x_{2},y_{2})$, point C have coordinates $(x_{3}, y_{3})$ and point D have coordinates $(x_{4},y_{4})$. When quadrilateral ABCD undergoes reflection across, quadrilateral A'B'C'D' is formed with coordinates of

A' = $(x_{1}, -y_{1})$

B' = $(x_{2}, -y_{2})$

C' = $(x_{3},-y_{3})$

D' = $(x_{4}, -y_{4})$

Now, A'B'C'D' is translated right by 3 units and up by 2 units to form quadrilateral A"B"C"D" with coordinates of

A" = $(x_{1}+3, -y_{1}+2)$

B" = $(x_{2}+3, -y_{2}+2)$

C" = $(x_{3}+3, -y_{3}+2)$

D" = $(x_{4}+3, -y_{4}+2)$

Final Answer:

Coordinates of A' and A" are $(x_{1}, -y_{1})$ and $(x_{1}+3, -y_{1}+2)$ respectively.