Translation Exploration by Leon Brin

Loading the math board and drawing, please wait…

2017-01-30 03:09

This example demonstrates the concept of translation. By using translation vectors, we can observe how points and shapes move on a plane. Key mathematical concepts include vectors and translation. GeoGebra commands used include AttachCopyToView, Vector, Translate, and Point. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

AttachCopyToView(PolyLine[(0.2748542981397276, 1.826564317740839), (0.28333625050717726, 1.8689740795780876), (0.2748542981397276, 1.8944199366804366), (0.24940844103737855, 1.9029018890478864), (0.2154806315675798, 1.9029018890478864), (0.18155282209778106, 1.9029018890478864), (0.156106964995432, 1.8944199366804366), (0.13914306026053264, 1.8689740795780876), (0.11369720315818359, 1.852010174843188), (0.08825134605583454, 1.826564317740839), (0.07976939368838486, 1.80111846063849), (0.07976939368838486, 1.7671906511686915), (0.09673329842328422, 1.7417447940663424), (0.11369720315818359, 1.7162989369639932), (0.13914306026053264, 1.7078169845965436), (0.1730708697303314, 1.7162989369639932), (0.20699867920013013, 1.724780889331443), (0.2324445363024792, 1.7417447940663424), (0.2578903934048282, 1.7587086988012417), (0.2748542981397276, 1.7841545559035907), (0.29181820287462695, 1.8096004130059398), (0.30030015524207665, 1.8350462701082888), (NaN, NaN), (0.45297529785617097, 1.9453116508851347), (0.41904748838637224, 1.9453116508851347), (0.3936016312840232, 1.936829698517685), (0.3681557741816741, 1.9198657937827857), (0.3596738218142244, 1.8944199366804366), (0.3511918694467748, 1.8689740795780876), (0.3511918694467748, 1.8350462701082888), (0.3596738218142244, 1.8096004130059398), (0.3851196789165735, 1.80111846063849), (0.41056553601892254, 1.7841545559035907), (0.44449334548872127, 1.7841545559035907), (0.47842115495852, 1.7841545559035907), (0.5123489644283188, 1.7841545559035907), (0.5377948215306678, 1.80111846063849), (0.5632406786330169, 1.8096004130059398), (0.5802045833679162, 1.8350462701082888), (0.5886865357353659, 1.8604921272106378), (0.5802045833679162, 1.8859379843129869), (0.5632406786330169, 1.911383841415336), (0.5377948215306678, 1.9283477461502354), (0.5123489644283188, 1.936829698517685), (0.47842115495852, 1.936829698517685), (NaN, NaN), (0.18155282209778106, 1.6738891751267448), (0.19851672683268043, 1.639961365656946), (0.2239625839350295, 1.6229974609220468), (0.24940844103737855, 1.6060335561871475), (0.2748542981397276, 1.589069651452248), (0.30878210760952635, 1.5721057467173487), (0.3342279647118754, 1.5551418419824492), (0.3596738218142244, 1.5466598896149997), (0.3936016312840232, 1.5466598896149997), (0.42752944075382193, 1.5466598896149997), (0.45297529785617097, 1.563623794349899), (0.47842115495852, 1.5805876990847982), (0.4869031073259697, 1.6060335561871475), (0.4869031073259697, 1.639961365656946), (0.4953850596934194, 1.665407222759295), (NaN, NaN), (0.3596738218142244, 2.0810228887643296), (0.30878210760952635, 2.097986793499229), (0.2748542981397276, 2.1064687458666786), (0.24092648866992886, 2.114950698234128), (0.19851672683268043, 2.123432650601578), (0.1645889173628817, 2.123432650601578), (0.13066110789308297, 2.123432650601578), (0.08825134605583454, 2.114950698234128), (0.06280548895348549, 2.1064687458666786), (0.04584158421858612, 2.0810228887643296), (0.028877679483686747, 2.0555770316619806), (0.01191377474878738, 2.0301311745596315), (-0.00505012998611199, 2.0046853174572825), (-0.013532082353561674, 1.9792394603549335), (-0.030495987088461043, 1.9537936032525844), (-0.03897793945591073, 1.9283477461502354), (-0.04745989182336041, 1.9029018890478864), (-0.055941844190810094, 1.8774560319455373), (-0.06442379655825978, 1.8350462701082888), (-0.06442379655825978, 1.80111846063849), (-0.06442379655825978, 1.7671906511686915), (-0.055941844190810094, 1.7417447940663424), (-0.04745989182336041, 1.7162989369639932), (-0.030495987088461043, 1.6908530798616441), (-0.02201403472101136, 1.665407222759295), (-0.013532082353561674, 1.639961365656946), (0.0034318223813376947, 1.614515508554597), (0.020395727116237064, 1.589069651452248), (0.03735963185113643, 1.563623794349899), (0.06280548895348549, 1.5466598896149997), (0.07976939368838486, 1.5212140325126506), (0.1052152507907339, 1.4957681754103016), (0.13066110789308297, 1.478804270675402), (0.14762501262798233, 1.453358413573053), (0.1730708697303314, 1.4448764612056033), (0.19851672683268043, 1.4363945088381538), (0.2154806315675798, 1.4109486517358047), (0.24092648866992886, 1.402466699368355), (0.28333625050717726, 1.3939847470009052), (0.31726405997697604, 1.3939847470009052), (0.3511918694467748, 1.3939847470009052), (0.3851196789165735, 1.402466699368355), (0.41904748838637224, 1.4109486517358047), (0.44449334548872127, 1.4194306041032543), (0.46993920259107036, 1.4363945088381538), (0.4953850596934194, 1.453358413573053), (0.5293128691632182, 1.4703223183079526), (0.5547587262655672, 1.4872862230428519), (0.5802045833679162, 1.5042501277777511), (0.5971684881028156, 1.5296959848801002), (0.6141323928377149, 1.5551418419824492), (0.6226143452051647, 1.5805876990847982), (0.6480602023075137, 1.6060335561871475), (0.6650241070424131, 1.6314794132894965), (0.6735060594098627, 1.6569252703918456), (0.6904699641447621, 1.6823711274941946), (0.7074338688796615, 1.7078169845965436), (0.7159158212471112, 1.7417447940663424), (0.7328797259820106, 1.775672603536141), (0.7328797259820106, 1.8096004130059398), (0.7328797259820106, 1.8435282224757386), (0.7328797259820106, 1.8774560319455373), (0.7159158212471112, 1.9029018890478864), (0.6904699641447621, 1.9198657937827857), (0.6650241070424131, 1.9453116508851347), (0.6480602023075137, 1.9707575079874837), (0.6226143452051647, 1.9792394603549335), (0.5971684881028156, 1.9962033650898328), (0.5717226310004666, 2.013167269824732), (0.5462767738981175, 2.021649222192182), (0.5208309167957684, 2.0301311745596315), (0.4953850596934194, 2.047095079294531), (0.46993920259107036, 2.0555770316619806), (0.44449334548872127, 2.06405898402943), (0.41904748838637224, 2.07254093639688), (0.3936016312840232, 2.0810228887643296), (NaN, NaN), (0.156106964995432, 1.8604921272106378), (0.13066110789308297, 1.8350462701082888), (0.14762501262798233, 1.8096004130059398), (0.1730708697303314, 1.7841545559035907), (0.20699867920013013, 1.7841545559035907), (0.20699867920013013, 1.8180823653733895), (NaN, NaN), (0.41904748838637224, 1.9283477461502354), (0.40208358365147284, 1.8944199366804366), (0.3936016312840232, 1.8689740795780876), (0.40208358365147284, 1.8435282224757386), (0.42752944075382193, 1.8350462701082888), (0.45297529785617097, 1.8435282224757386), (NaN, NaN), (0.07976939368838486, 2.038613126927081), (0.04584158421858612, 2.021649222192182), (0.020395727116237064, 2.0046853174572825), (0.0034318223813376947, 1.9792394603549335), (-0.013532082353561674, 1.9537936032525844), (-0.02201403472101136, 1.9283477461502354), (-0.013532082353561674, 1.9029018890478864), (-0.013532082353561674, 1.852010174843188), (-0.02201403472101136, 1.8180823653733895), (NaN, NaN), (0.30030015524207665, 2.07254093639688), (0.3427099170793251, 2.047095079294531), (0.3681557741816741, 2.038613126927081), (0.3936016312840232, 2.021649222192182), (0.41904748838637224, 2.013167269824732), (0.44449334548872127, 1.9962033650898328), (0.46993920259107036, 1.9792394603549335), (0.4953850596934194, 1.962275555620034), (NaN, NaN), (0.07128744132093517, 2.1658424124388262), (0.0543235365860358, 2.1997702219086253), (0.028877679483686747, 2.2167341266435248), (0.0034318223813376947, 2.2252160790109743), (-0.02201403472101136, 2.233698031378424), (-0.055941844190810094, 2.233698031378424), (-0.08138770129315916, 2.2252160790109743), (NaN, NaN), (0.1052152507907339, 2.1573604600713767), (0.11369720315818359, 2.1912882695411753), (0.13066110789308297, 2.2167341266435248), (0.14762501262798233, 2.242179983745874), (0.18155282209778106, 2.259143888480773), true], 1, (-0.8702092714659798, -0.7519492019638644), (4.023877244552488, 2.5051205071368137), (316.5440893920006, 510.24454032400075), (893.5440893920003, 126.24454032400082)) → stroke1
Vector(A, B) → u
Translate(stroke1, u) → stroke1'
Point(stroke1) → C
Translate(C, u) → C'
Vector(C, C') → v
Vector(D, E) → w
Translate(stroke1, w) → stroke1'_1

AI Drawing Prompt Reference

Draw a shape composed of multiple line segments. First, draw a polygon, then translate the polygon using a vector to observe the translation effect. Next, pick a point on the polygon and translate it using the same vector. Then, connect the translated point to the original point with a vector. Finally, draw another vector and translate the polygon again, this time using the new vector.

The prompt above was compiled from the original drawing commands and is for reference only.