Answer: The correct option is
(A) Quadrilateral 1 and quadrilateral 2 are congruent because quadrilateral 2 can be created by rotating and then translating quadrilateral 1.
Step-by-step explanation: We are given to select the statement that best describes the quadrilaterals shown in the figure.
From the graph, we note that
the co-ordinates of the vertices of quadrilateral 1 are (3, -2), (1, -3), (2, -7) and (6, -5).
And, the co-ordinates of the vertices of quadrilateral 2 are (-3, 2), (-4, 4), (-8, 3) and (-6, -1).
We see that if quadrilateral 1 is rotated 90° clockwise and then translated 5 units upwards, 1 unit left, then its vertices changes according to the following rule :
(x, y) ⇒ (y, -x) ⇒ (y-1, -x+5).
That is,
(3, -2) ⇒ (-2, -3) ⇒ (-2-1, -3+5) = (-3, 2),
(1, -3) ⇒ (-3, -1) ⇒ (-3-1, -1+5) = (-4, 4),
(2, -7) ⇒ (-7, -2) ⇒ (-7-1, -2+5) = (-8, 3),
(6, -5) ⇒ (-5, -6) ⇒ (-5-1, -6+5) = (-6, -1).
Therefore, the co-ordinates of the vertices of quadrilateral 2 can be obtained from the co-ordinates of the vertices of quadrilateral 1 by applying the following two transformations :
rotation of 90° clockwise and then translation 5 units upwards, 1 unit to the left.
Since rotation and translation does not change the size of the quadrilateral, so quadrilaterals 1 and 2 are congruent.
Thus, quadrilateral 1 and quadrilateral 2 are congruent because quadrilateral 2 can be created by rotating and then translating quadrilateral 1.
Option (A) is CORRECT.
