.11 4736 5:22 PM 7: Problem 10 Previous Problem List Next (1 point) Let T, be th
ID: 3136937 • Letter: #
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.11 4736 5:22 PM 7: Problem 10 Previous Problem List Next (1 point) Let T, be the reflection about the line -6x + 3y 0 and T2 be the reflection about the line -4x 5y 0 in the euclidean plane. (i) The standard matrix of T o T2 is: Thus TT, is a counterclockwise rotation about the origin by an angle of radians. (ii) The standard matrix of T2 o T1 is: Thus T2 o T1 is a counterclockwise rotation about the origin by an angle of radians. Note: You can earn partial credit on this problem Preview My Answers Submit Answers You have attempted this problem 0 times. You have unlimited attempts remaining Email instructor K-Explanation / Answer
The standard matrix for the linear transformation for reflection about the line y = mx is
(1-m2)/(1+m2)
2m/(1+m2)
2m/(1+m2)
(m2-1)/ (1+m2)
Thus, the standard matrix for T1,which reflects about the line -6x+3y = 0 oy, 3y = 6x or, y = 2x is A =
-3/5
4/5
4/5
3/5
Also, the standard matrix for T2,which reflects about the line -4x+5y = 0 or, 5y = 4x or, y = (4/5)x is B =
9/41
40/41
40/41
-9/41
The standard matrix of T1oT2 is AB =
133/205
-156/205
156/205
133/205
The matrix for counterclockwise rotation about the origin by an angle is
cos
-sin
sin
cos
Hence = cos-1(133/205) = 49.550 = = 0.275 radians(approximately).( note: sin-1 156/205 ia also = 49.550 )
The standard matrix of T2oT1 is BA =
133/205
156/205
-156/205
133/205
Hence T2oT1 is counterclockwise rotation about the origin by an angle tan-1 (-156/133) = -49.550 = -0.275 radians (approximately).
(1-m2)/(1+m2)
2m/(1+m2)
2m/(1+m2)
(m2-1)/ (1+m2)
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