Complete the statement about the figures in the graph. Quadrilateral ABCD undergoes a __________to form quadrilateral A'B'C'D'.
Answers
Answer:
Answer: The correct option is (C) reflection across the X-axis.
Step-by-step explanation: We are given to select the correct option that will complete the following statement.
"Quadrilateral ABCD undergoes a ? to form quadrilateral A'B'C'D'".
The co-ordinates of the vertices of quadrilateral ABCD are
A(3, 4), B(4, 3), C(5, 1) and D(1, 2).
And the co-ordinates of the vertices of quadrilateral A'B'C'D' are
A'(3, -4), B'(4, -3), C'(5, -1) and D'(1, -2).
We can see the the y-co-ordinate in the vertices of quadrilateral A'B'C'D' are negative of the y-co-ordinate of the vertices of quadrilateral ABCD.
Therefore, the quadrilateral ABCD undergoes the transformation y = -y to form quadrilateral A'B'C'D'.
We have
\begin{lgathered}y=-y\\\\\Rightarrow y+y=0\\\\\Rightarrow 2y=0\\\\\Rightarrow y=0,\end{lgathered}y=−y⇒y+y=0⇒2y=0⇒y=0,
which is the equation of X-axis.
Thus, the correct transformation is (C) reflection across X-axis.
And the complete statement is
"Quadrilateral ABCD undergoes a reflection across X-axis to form quadrilateral A'B'C'D".
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