Congruence Transformation

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Congruence transformation is a useful tool Transformations are of 3 type rotation (turn), reflection (flip) and translation (slide).
After transformation the area, shape, angles and line length remains the same. These shapes formed after turning, flipping
and/or sliding and the initial shapes are both called congruent. This transformation from one form to other is called
congruence transformation. During transformation every point of the object moves in the same direction and same distance.
The following 2 examples will help to better understand congruence transformation.

Example 1: Explain the sequence of transformation from figure 1 to 2.

 Figure 1 coordinates are (-4, 3), (-1, 3), (-4, 1) and (-1, 1)


Figure 2 coordinates are (1, 4), (3, 4), (3, 1) and (1, 1)

Solution: In the given problem

 Figure 1 is a square which when forms a mirror image towards right

 (-4, 3), (-1, 3), (-4, 1) and (-1, 1) = (4, 3), (1, 3), (4, 1) and (1, 1)

 Then rotated 90 degrees around the point (1,1)

 (4,3), (1,3), (4,1) and (1,1)  = (1,4), (3,4), (1,3) and (1,1), we get Figure 2

 
Example 2: Explain the sequence of transformation from figure 1 to 2.

Figure 2 coordinates are (2, 1), (2, 2) and (3, 1)

Solution: In the given problem

Figure 1 is a triangle which when flipped towards right it forms a mirror image

(1,0), (1,1) and (0,0) = (1,0), (1,1) and (2,0)

Then this figure is moved, we get figure 2

(1,0), (1,1) and (2,0) = (2,1), (2,2) and (3,1).


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