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Transformations in geometry

The document discusses different types of geometric transformations including translations, reflections, and rotations. It provides examples of translating triangles by moving their vertices in different directions and distances, which results in congruent triangles of the same size and shape. Translations involve sliding the figure along the plane without changing its size or orientation. Reflections involve flipping the figure across a mirror line, also producing a congruent image. Rotations turn the figure around a center point, keeping each point the same distance from the center.

Education◦
By Michael Sithole 201114682
Rotation Turn! Reflection Flip! Translation Slide! After any of those transformations (turn, flip or slide), the shape still has the same size, area, angles and line lengths.
 Let us first revise the plotting of points on the cartesian plane.  Plot the following points on the grid provided.  A(2;4), B(-3;6),C(-5;-6),  D(6;-4)  Now translate each point 2 units to the right and 1 unit downward.
 Consider ∆ABC in the figure alongside.  ∆ABC has been translated 10 units to the left to form the image ∆A’B’C’.  You will notice that the three vertices of the ∆ABC has moved 10 units to the left.  A has moved 10 units left to form A’.  B has moved 10 units left to form B’.  C has moved 10 units left to form C’.  ∆ABC is congruent to ∆A’B’C’. They are identical in size and shape.
 Consider ∆ABC in the figure below.  ∆ABC has been translated 9units downwards to form the image ∆A’B’C’.  You will notice that the three vertices of the ∆ABC has moved 9units downward.  A has moved 9 units downward to form A’.  B has moved 9 units downward to form B’.  C has moved 9 units downward to form C’.  ∆ABC is congruent to ∆A’B’C’. They are identical in size and shape.
 In this example, ABC has first translated 11 units to the left and then 9 units downwards.  Notice that the three vertices have moved 11 units to the left and then 9 units downwards.  A has moved 11 units to the left and then 9 units downward to form A‘  B has moved 11 units to the left and then 9 units downward to form B‘  C has moved 11 units to the left and then 9 units downward to form C‘  Clearly, figure ABC is congruent to A'B'C’ since they are identical in size and shape.
 Translate figure ABCD as follows 9 units to the left and 1 unit upwards.  Translate A’B’C’D’ as follows 1 unit to the right and 9 units downward.
"Rotation" means turning around a center: The distance from the center to any point on the shape stays the same. Every point makes a circle around the center.
Every point is the same distance from the central line ! ... and ... The reflection has the same size as the original image The central line is called the Mirror Line ...
1. Measure from the point to the mirror line (must hit the mirror line at a right angle) 2. Measure the same distance again on the other side and place a dot. 3.Then connect the new dots up!
Resizing The other importantTransformation is Resizing (also called dilation, contraction, compression, enlargement or even expansion).The shape becomes bigger or smaller: Resizing Resize! If you have to use Resizing to make one shape become another then the shapes are not Congruent, they are Similar.