The equation of a line (L) is Y=x/2 + 2.vertices of the triangle ABC are given in homogeneous co-ordinates as A(2, 4, 1), B(4, 6, 1) and C(2, 6, 1).

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written 6.2 years ago by

teamques10 ★ 68k

• modified 2.8 years ago

Find a composite transformation matrix that will reflect triangle ABC about the line (L) and also find its new co-ordinates.

Mumbai university > mechanical engineering > sem 7 > cad/cam/cae

Marks : 10M

Difficulty : Easy

cad cam cae

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written 6.2 years ago by

teamques10 ★ 68k

enter image description here

Equation of line is : enter image description here

Comparing with enter image description here

Also enter image description here

enter image description here

Step 1: Transformation of Point P(0,2) to origin O(0,0)

enter image description here (-ve as direction is downward.)

Step 2: Rotation of line by an angle of θ = -36.87o (-ve as it is moving in clockwise direction)

enter image description here

Step 3: Reflection of triangle about x-axis

Matrix for reflection about x-axis is given as,

enter image description here

Step 4: Inverse rotation of line to its original angle

enter image description here

Step 5: Inverse Translation of Point P to its original position

enter image description here (+ve as direction is upwards)

Now, The composite transformation matrix, enter image description here =

Now, new coordinate of triangle ABC are

[X'] = [X] [T]

enter image description here

A' = (2.7, 2.3)

B' = (5.5, 2.7)

C' = (4.3, 1.1)

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