Figure [R] was rotated about the origin [(0,0)] by [270^\circ] clockwise. Which figure is the image of [R]?
A. A coordinate plane with 2 quadrilaterals. Quadrilateral R has vertices at (0, 7), (7, 4), (5, 4), and (5, 2). Quadrilateral R is rotated to form quadrilateral A. Quadrilateral A has vertices at (7, 0), (4, negative 7), (4, negative 5), and (2, negative 5).
B. A coordinate plane with 2 quadrilaterals. Quadrilateral R has vertices at (0, 7), (7, 4), (5, 4), and (5, 2). Quadrilateral R is rotated to form quadrilateral B. Quadrilateral B has vertices at (0, negative 7), (5, negative 2), (5, negative 4), and (7, negative 4).
Answer (2)
To solve this problem, we need to understand the effect of rotating a figure on the coordinate plane. Here, we're dealing with a 270° clockwise rotation about the origin (0,0).
When a point ( x , y ) is rotated 270° clockwise, it transforms to ( y , − x ) . Let's apply this transformation to each vertex of Quadrilateral R :
Vertex: (0, 7)
New Position: ( 7 , 0 )
Vertex: (7, 4)
New Position: ( 4 , − 7 )
Vertex: (5, 4)
New Position: ( 4 , − 5 )
Vertex: (5, 2)
New Position: ( 2 , − 5 )
Now, let's check the options:
Choice A : Quadrilateral A has vertices ( 7 , 0 ) , ( 4 , − 7 ) , ( 4 , − 5 ) , ( 2 , − 5 ) .
Choice B : Quadrilateral B has vertices ( 0 , − 7 ) , ( 5 , − 2 ) , ( 5 , − 4 ) , ( 7 , − 4 ) .
From our calculations, it matches that Quadrilateral A is the image of R after a 270° clockwise rotation.
So, the correct answer is Choice A .
The image of Quadrilateral R after a 270° clockwise rotation about the origin is Quadrilateral A, which has vertices at (7, 0), (4, -7), (4, -5), and (2, -5).
;
