Question

(d) (3 pts) T: R2 + R2 first reflects points through the 11-axis and then reflects points through the line 22 = 11 (e) (3 pts) T:R2 + R2 first reflects points through the 11-axis and then reflects points through the 22-axis.

Answer 1

Questim nord solution :- Here re given given mapping of lineas transformation mapping o Is T R² R² of we reflects points through ne axis there this trous formation is defined as T (20; *z) = (2,-22) 1. Then Tln, 12) = [10] ) I PqCX, Me) or T(m) - Ax more a= [2] . o Here Azrio] is the pib (2, 42) Standard matrix. (Reflection about X, axis.) Now if we reflex this transformation about the line man, then Trons formation will be T(*+-+2) = (-22, *1) 7m7 l since reflxction To about a is T (2182) = (*2,21) Here standard matrix is 10-1 ] 1 -1 ] @ Now from the part-(d) we see that of refluxts points throuhy sy axis then Transformation will be T(*1, 12) = (2,42) Now we reflects this points through sy on's then T(*, -H2) = (-2,-42) This the points th, affinally maps to the points (-21, 12) ie T(2,;42) = (-4,-22) Standard mathia beto. 97 6:16] O

1. So graph will be po/?-myths -ke) . * Here also first we reflects the points (*, ;k2) thronk the sean's then fooms formation will be T(mo, R2) = (x,-H2) Now we rotates points -11/2 radians. Now we now that for argoya points (x, y) ERR rotate through an ongle o . Then fons fomatin will be Te (nry) = (acoso-ysing a sino ty coso) so if the points (R,,K2) rotates through an ongle -7/2 , then trong formation will be TR (91,-22 ) = (x2 6036172) +2sthf-7%), aysinlogl-x.co54-72 z (0-22; -24) = (-22,-3) Thus finally the points (m, 22) maps to the points fm2,-21). le TR ( 2 , K2) 2 (M2; 26) 1. - to-17rmy 1-OJCXL (x, 22) - standard makiy s rony 2 te Answer . (-X1,5X2)
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