Question

Complete the statement about the figures in the graph. Quadrilateral ABCD undergoes a __________to form quadrilateral A'B'C'D'.

translation 2 units down


90°clockwise rotation


reflection across the x-axis


reflection across the y-axis

Answer 1

It’s a reflection across the x axis

Answer 2

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

`y=-y\\\\\Rightarrow y+y=0\\\\\Rightarrow 2y=0\\\\\Rightarrow 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".