Reflect the triangle ABC about the line 3x-4y+8=0. The position vector of the coordinate ABC is given as A=(4,1), B=(5,2),C=(4,3). Find the composite transformation matrix and its new coordinates.

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written 6.2 years ago by

teamques10 ★ 68k

• modified 2.8 years ago

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 3x - 4y + 8 = 0 ,i.e; 4y = 3x + 8

i.e; y = (3/4)x + 2

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: Reverse 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' = (0.16, 6.12)

B' = (1.4, 6.8)

C' = (2.08, 5.56)

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