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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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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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Then the final position of point A is

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

y = x

(II) Translation through a distance

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(III) Rotation of coordinate axes through an angle

\frac{π}{4}

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The final position of the point is given by the coordinates

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undergoes following transformations successively :
(i) reflection about line

y = x

(ii) translation through a distance of

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(iii) rotation through an angle

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