TG0-M Mira Activities: Using the mira* 7The mira is a mirror through w hich you can see (to the other side of the mirror). This allows you to perceive the reflected image in the mira as actually being on the other side. MA1. Place the mira between points A & B so that the image of AB is on itself, and B’s image is on A. The mira must be perpendicular to the paper, with its beveled edge at the bottom, facing you. Trace t he line at the beveled edge. This is the mirror line " l". The reflection of A through l is B. (by the w ay, how is the line l relat ed t o segment A B?) C AB CMA2. Place the mira between the 1 & 2 triangles above. Experiment w it h the placement of the mira.st ndIs one t he ref lect ion of t he ot her? What about the second and the third? mMA3. The mira can be used for drawing reflected images. Place the mira line on the mirror line m, and trace !the image of the figure F reflected through m.Many of the constructions w e have done with compass &straightedge involved bisectors and perpendicular lines. These const ructions can be very simple w it h the mira.P CC QUSE THE MIRA TO FIND:MA4. the perpendicular bisector of the line segment PQ.MA5. the bisector of the angle RST.MA6. the center O of the circle C.MA7. the altitude of triangle DEF passing through D. R @CS @ TD E @ @ @ F GTG-1 ! MATH 310 " TRANSFORM ATIONAL GEOM ETRY # 7 A translation of t he plane is one kind of isometry– in w hich the vector (directed line segment,or arrow ) joining each point to its image is constant (the same).In effect, all points slide per one vector (w hich our text calls the " slide arrow " ). After translation, the image of a figure in the plane is congruent to the original. Notice sinceevery point moves the same way, t he original & image face the same direction in the plane. T1. Find the image of figure " A" under the translation indicated by vector " U" . Label t he image A'.Hint : Locat e key point s, and see w here t he translation vector moves each one.T2* . Next translate the figure A' (NOT A) by the vector " V" , to f igure A''. T3* . You have just found t he image of A under the composition of the two translations, U follow ed by V. [The notation for this composition is VBU.] r What transformation of the plane w ould move figure A directly to A''?T4. Can you f ind a translation of the plane (ie find the vector of translation), that transforms figure B to B’ ? C to C' ? D to D’? UV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . …