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
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1 |
0 |
0 |
|||
|
3 |
2 |
1 |
* |
0 |
-1 |
0 |
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|
0 |
0 |
1 |
|||
|
= |
3 |
-2 |
1 |
B
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-1 |
0 |
0 |
|||
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3 |
2 |
1 |
* |
0 |
1 |
0 |
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|
0 |
0 |
1 |
|||
|
= |
-3 |
2 |
1 |
C
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|
-1 |
0 |
0 |
|||
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3 |
2 |
1 |
* |
0 |
-1 |
0 |
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|
0 |
0 |
1 |
|||
|
= |
-3 |
-2 |
1 |
D
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0 |
1 |
0 |
|||
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3 |
2 |
1 |
* |
1 |
0 |
0 |
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0 |
0 |
1 |
|||
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= |
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)].
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
