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Two Circles Touching Internally and Externally

T : R2→ R2 fi...

Question

$T : R^{2} \to R^{2}$ first rotates points through $- \frac{3 π}{4}$ radian (clockwise) and then reflects points through horizontal x-axis.

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Solution

A = R_y=xR_30°CW
= ⌈0 1⌉ ⌈√3/2 1/2⌉
⌊1 0⌋ ⌊−1/2 √3/2⌋
= ⌈−1/2 √3/2⌉
⌊√3/2 1/2⌋

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(ii) translation through a distance of

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(iii) rotation through an angle

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Q. The point A(4, 1) undergoes following transformations successively
(i) reflection about line y = x
(ii) translation through a distance of 2 units in the positive direction of x axis
(iii) rotation through an angle

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in anti clockwise direction about origin O
Then the final position of point A is

(4, 1)

undergoes the following three transformations successively:
(I) Reflection about the line

y = x

(II) Translation through a distance

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units along the positive direction of

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(III) Rotation of coordinate axes through an angle

\frac{π}{4}

about the origin in the clockwise direction.
The final position of the point is given by the coordinates

A (4, 1)

undergoes following transformations successively :
(i) reflection about line

y = x

(ii) translation through a distance of

3

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x

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(iii) rotation through an angle

105^{\circ}

in anti-clockwise direction about origin

O

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Then the final position of point

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(b) Transformation through a distance $2$ units along the positive direction of the x-axis.

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The final position of the point is given by the co-ordinates

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