2. Select all transformations that must take any point A to any point B.
A. Rotation of 180° around A
B. Rotation of 180°around B
C. Rotation of 180° around the midpoint of segment AB
D. Reflection across the line AB
E. Reflection across the perependicular bisector of segment AB
F. Translation by the directed line segment AB
G. Translation by the directed line segment BA
Answers
The given transformation of reflection, rotation and translation are rigid transformation
The transformation that must take any point A to any point B are;
Rotation of 180° around the midpoint of segment ABReflection across the perpendicular bisectorTranslation by the directed line segment ABReason:
Question: The given quadrilaterals ABCD and A'B'C'D' are congruent
Required; To select all transformation that must take a point A to point B
Solution:
Rotation of 180° around the midpoint of segment ABA rotation of 180° about the midpoint of segment AB will change the places of points A and B
A(x, y) → R₁₈₀ → A'(-x, -y)
Let the coordinates of the origin be the midpoint of segment AB, and let (x, y) represent the coordinate of the point B(x, 0) we have;
∴ The coordinates of point A is A(-x, 0), which gives;
A(-x, 0) → R₁₈₀ → A'(x, 0) = point B
Therefore a rotation about the midpoint of AB must take point A to point B
Reflection across the perpendicular bisectorThe reflection of a point (x, y) about y-axis gives a point (-x, y), therefore, we have;
A(-x, 0) → Reflection across the y-axis → A'(x, 0) = point B
Therefore, a reflection across the perpendicular bisector of the line AB must take the point A to point B
Translation by the directed line segment ABA translation along the directed line segment AB of point A(-x, 0) 2·x units right gives;
A'(-x + 2·x, 0) = A'(x, 0) = Point B
Therefore, the transformations that must take any point A to any point B are;
Rotation of 180° around the midpoint of segment AB
Reflection across the perpendicular bisector
Translation by the directed line segment AB
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