The Correct statements are as follows:-
- Statement(b) A reflection of shape-I across X-axis followed by 90° in clockwise rotation about the origin.
- Statement(d) A reflection of shape-I across Y-axis followed by a 90° clockwise rotation about the origin.
Here we need to select the correct set of Statements that signifies the congruence of shape-II and shape-I in the given diagram.
- The co-ordinates of Vertices of shape I are (0, -10), (2, -8), (12,-4) and (10, -8).
- The co-ordinates of vertices of shape II are (-10, 0), (-8, 2), (-4, 12) and (-8, 10).
There are two possible Sets of Transformations:
Case I 1st Reflection across X-axis and then rotation of 90° in clockwise direction about the origin.
After reflection across X-axis, the the Y co-ordinate of each vertex will change its sign (y = -y). So, the vertices becomes
(0, 10), (2, 8), (12,4) and (10, 8).
Here, After it rotates 90° counterclockwise about the origin, then the rule needs to be applied to all the vertices are,
(x, y) ⇒ (-y, x).
So, The overall vertices are
(0, 10) ⇒ (-10, 0),
(2, 8) ⇒ (-8, 2),
(12, 4) ⇒ (-4, 12),
(10, 8) ⇒ (-8, 10).
These are the vertices of shape II. Therefore statement 2 is TRUE.
Case II : 1st Reflection across Y-axis and then rotation of 90° in clockwise direction about the origin
After reflection across Y-axis, the the X co-ordinate of each vertex will change its sign(x = -x). So, the vertices becomes
(0, -10), (-2, -8), (-12, -4) and (-10, -8).
Here After it rotates 90° counterclockwise about the origin, then the rule needs to be applied to all the vertices are
(x, y) ⇒ (y, -x).
Hence, Final vertices will be :-
(0, -10) ⇒ (-10, 0),
(-2, -8) ⇒ (-8, 2),
(-12, -4) ⇒ (-4, 12),
(-10, -8) ⇒ (-8, 10).
These are the vertices of shape II. Therefore statement D is TRUE.
Therefore,
- Shape I lies in Quadrant IV
- Shape II lies in Quadrant II.
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