Which transformations can be used to carry ABCD onto itself? The point of rotation is (3, 2). Check all that apply.A.Translation two units upB.Rotation of 90C.Rotation of 180D.Reflection across the line y = 2
Question
Which transformations can be used to carry ABCD onto itself? The point of rotation is (3, 2). Check all that apply.A.Translation two units upB.Rotation of 90C.Rotation of 180D.Reflection across the line y = 2
Solution
To determine which transformations can carry quadrilateral ABCD onto itself with a point of rotation at (3,2), we need to consider each option:
A. Translation two units up: This transformation would move every point in the quadrilateral two units up. If ABCD is symmetric about the line y=2, then this transformation would carry ABCD onto itself. Otherwise, it would not.
B. Rotation of 90 degrees: A rotation of 90 degrees about the point (3,2) would not carry ABCD onto itself unless ABCD is a square or a circle centered at (3,2).
C. Rotation of 180 degrees: A rotation of 180 degrees about the point (3,2) would carry ABCD onto itself if ABCD is symmetric about the point (3,2).
D. Reflection across the line y = 2: This transformation would carry ABCD onto itself if ABCD is symmetric about the line y=2.
Without more information about the shape and orientation of ABCD, it's impossible to definitively say which transformations would carry ABCD onto itself. However, these are the conditions under which each transformation would work.
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