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Example Two Dimension Reflect

 Example Two Dimension Reflect


Example 1 /: Reflect the point P(3,2) in A- X axis; B- Y axis; Corigin; D-line Y=X;

sol //

A

 

1

0

0

3

2

1

*

0

-1

0

 

0

0

1

=

3

-2

1



B


 

-1

0

0

3

2

1

*

0

1

0

 

0

0

1

=

-3

2

1


C


 

-1

0

0

3

2

1

*

0

-1

0

 

0

0

1

=

-3

-2

1


D

 

0

1

0

3

2

1

*

1

0

0

 

0

0

1

=

2

3

1




Example 2/What (3*3) matrix will change the center of the scene to the origin, and reflect the mountains in the lake? [The center of the scene is (4, 0)].



sol//




Example 3/ Find the single matrix that causes all the points in the plane to be reflected in the line with equation Y=0.5X+2, then apply this matrix to reflect the triangle with vertices at A(2,4), B(4,6), C(2,6) in the line.

sol//

The Cartesian equation of a line in 2D is Y= M * X +b where b is the intersection of the lint with the Y-axis and M is a gradient of the line M= ΔY / ΔX = Tan Ǿ

 

So the line Y=0.5 X + 2 has gradient M= 0.5 and intersect with the Y-axis at the point where y=2

So K=2 , Tan Ǿ =0.5  Ǿ=26.57

2Ǿ=53.13 , Cos 2Ǿ=0.6 , Sin 2Ǿ=0.8






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