the vertex of a figure is located at (2, 4). the figure is rotated and the image of the vertex is located at (-2, -4). which of these describes the transformation?
a. rotation of 270 degrees anti-clockwise
b. rotation of 180 degrees anti-clockwise
c. reflection over the y-axis
d. reflection over the x-axis
Answers
Given : Image of ( 2, 4) is ( -2 , - 4)
To find : which of these describes the transformation?
a. rotation of 270 degrees anti-clockwise
b. rotation of 180 degrees anti-clockwise
c. reflection over the y-axis
d. reflection over the x-axis
Solution:
Point ( x , y)
If the point is rotated 90° anti-clockwise , the coordinates of the image will be (-y , x)
If the point is rotated 180° anti-clockwise , the coordinates of the image will be (-x , -y)
If the point is rotated 270° anti-clockwise , the coordinates of the image will be ( y , -x)
point ( x , y) . reflected over the x-axis will be ( x , - y)
point ( x , y) . reflected over the y-axis will be ( -x , y)
( 2, 4) is ( -2 , - 4)
=> (x , y) became ( -x , - y)
Hence rotation of 180 degrees anti-clockwise is correct answer
Correct answer is option b) rotation of 180 degrees anti-clockwise
Note : rotation of 180 degrees ( clock wise and anticlockwise result in same )
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