In inkscape i made this set of equilateral triangles, I would like to have each triangles's low vertex (the one that points to the bottom left) to undergo a variation of 5 px, so that it will actually have that vertex point 5 px more towards the direction its currently pointing
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<!-- Modified with equilateral triangles preserving original orientation -->

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    <!-- 
         For each triangle:
         • Compute centroid = ( (x₁+x₂+x₃)/3, (y₁+y₂+y₃)/3 ).
         • Let v = (apex – centroid) (apex = vertex with smallest y).
         • Then new triangle vertices are:
             p₁ = centroid + rot(v, +120°)
             p₂ = centroid + rot(v, –120°)
             p₃ = apex (unchanged)
         • Order the points (p₁, p₂, p₃) so that the apex remains the last vertex as in your original file.
         (In our examples the rotation yields an offset of approximately (28.08274, –7.53031) and (–7.53031, 28.08274) to add to the centroid.)
    -->
    
    <!-- Path1 
         Original vertices:
         A = (54.77922,54.18902), B = (23.95060,85.01764), Apex = (8.53627,38.77475)
         Centroid ≈ (29.08870,59.32714), v ≈ (–20.55243,–20.55239)
         New vertices:
         p₁ = (29.08870 + 28.08274, 59.32714 – 7.53031) = (57.17144,51.79683)
         p₂ = (29.08870 – 7.53031, 59.32714 + 28.08274) = (21.55839,87.40988)
         p₃ = (8.53627,38.77475)
    -->
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   d="M 57.17144,51.79683 L 21.55839,87.40988 L 8.53627,38.77475 Z" />
       
    <!-- Path2
         Original: A = (54.77926,201.32995), B = (23.95064,232.15857), Apex = (8.53623,185.91568)
         Centroid ≈ (29.08871,206.46807), v ≈ (–20.55248,–20.55239)
         New:
         p₁ ≈ (29.08871+28.08274, 206.46807–7.53031) = (57.17145,198.93776)
         p₂ ≈ (29.08871–7.53031, 206.46807+28.08274) = (21.55840,234.55081)
         p₃ = (8.53623,185.91568)
    -->
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   d="M 57.17145,198.93776 L 21.55840,234.55081 L 8.53623,185.91568 Z" />
       
    <!-- Path3
         Original: A = (124.47631,54.18901), B = (93.64768,85.01763), Apex = (78.23323,38.77476)
         Centroid ≈ (98.78574,59.32713), v ≈ (–20.55251,–20.55237)
         New:
         p₁ ≈ (98.78574+28.08274, 59.32713–7.53031) = (126.86848,51.79682)
         p₂ ≈ (98.78574–7.53031, 59.32713+28.08274) = (91.25543,87.40987)
         p₃ = (78.23323,38.77476)
    -->
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   id="path3"
   style="fill:#000000;stroke-width:2.42212"
   sodipodi0:nodetypes="ccc"
   d="M 126.86848,51.79682 L 91.25543,87.40987 L 78.23323,38.77476 Z" />
       
    <!-- Path4
         Original: A = (263.87016,54.18906), B = (233.04153,85.01768), Apex = (217.62711,38.77471)
         Centroid ≈ (238.17960,59.32715), v ≈ (–20.55249,–20.55244)
         New:
         p₁ ≈ (238.17960+28.08274, 59.32715–7.53031) = (266.26234,51.79684)
         p₂ ≈ (238.17960–7.53031, 59.32715+28.08274) = (230.64929,87.40989)
         p₃ = (217.62711,38.77471)
    -->
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   id="path4"
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   d="M 266.26234,51.79684 L 230.64929,87.40989 L 217.62711,38.77471 Z" />
       
    <!-- Path5
         Original: A = (54.77929,127.75949), B = (23.95066,158.58813), Apex = (8.53620,112.34519)
         Centroid ≈ (29.08871,132.89760), v ≈ (–20.55251,–20.55241)
         New:
         p₁ ≈ (29.08871+28.08274, 132.89760–7.53031) = (57.17145,125.36729)
         p₂ ≈ (29.08871–7.53031, 132.89760+28.08274) = (21.55840,160.98034)
         p₃ = (8.53620,112.34519)
    -->
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   id="path5"
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   sodipodi0:nodetypes="ccc"
   d="M 57.17145,125.36729 L 21.55840,160.98034 L 8.53620,112.34519 Z" />
       
    <!-- Path6
         Original: A = (194.17310,54.18905), B = (163.34448,85.01767), Apex = (147.93031,38.77472)
         Centroid ≈ (168.48263,59.32715), v ≈ (–20.55232,–20.55243)
         New:
         p₁ ≈ (168.48263+28.08274, 59.32715–7.53031) = (196.56537,51.79684)
         p₂ ≈ (168.48263–7.53031, 59.32715+28.08274) = (160.95232,87.40989)
         p₃ = (147.93031,38.77472)
    -->
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   d="M 196.56537,51.79684 L 160.95232,87.40989 L 147.93031,38.77472 Z" />
       
    <!-- Path7
         Original: A = (124.47623,127.75946), B = (93.64764,158.58809), Apex = (78.23330,112.34523)
         Centroid ≈ (98.78572,132.89759), v ≈ (–20.55243,–20.55236)
         New:
         p₁ ≈ (98.78572+28.08274, 132.89759–7.53031) = (126.86846,125.36728)
         p₂ ≈ (98.78572–7.53031, 132.89759+28.08274) = (91.25541,160.98033)
         p₃ = (78.23330,112.34523)
    -->
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   style="fill:#000000;stroke-width:2.42212"
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   d="M 126.86846,125.36728 L 91.25541,160.98033 L 78.23330,112.34523 Z" />
       
    <!-- Path8
         Original: A = (124.47621,201.33006), B = (93.64761,232.15867), Apex = (78.23332,185.91569)
         Centroid ≈ (98.78571,206.46814), v ≈ (–20.55240,–20.55245)
         New:
         p₁ ≈ (98.78571+28.08274, 206.46814–7.53031) = (126.86845,198.93783)
         p₂ ≈ (98.78571–7.53031, 206.46814+28.08274) = (91.25540,234.55088)
         p₃ = (78.23332,185.91569)
    -->
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   d="M 126.86845,198.93783 L 91.25540,234.55088 L 78.23332,185.91569 Z" />
       
    <!-- Path9 
         Origin (using relative coordinates; converted here to absolute):
         A = (263.87019,201.32993), B = (233.04157,232.15854), Apex = (217.62731,185.91564)
         Centroid ≈ (238.17969,206.46804), v ≈ (–20.55238,–20.55240)
         New:
         p₁ ≈ (238.17969+28.08274, 206.46804–7.53031) = (266.26243,198.93773)
         p₂ ≈ (238.17969–7.53031, 206.46804+28.08274) = (230.64938,234.55078)
         p₃ = (217.62731,185.91564)
    -->
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   d="M 266.26243,198.93773 L 230.64938,234.55078 L 217.62731,185.91564 Z" />
       
    <!-- Path10 
         Original (converted from relative):
         A = (263.86998,127.75949), B = (233.04138,158.58810), Apex = (217.62718,112.34522)
         Centroid ≈ (238.17951,132.89760), v ≈ (–20.55233,–20.55238)
         New:
         p₁ ≈ (238.17951+28.08274, 132.89760–7.53031) = (266.26225,125.36729)
         p₂ ≈ (238.17951–7.53031, 132.89760+28.08274) = (230.64920,160.98034)
         p₃ = (217.62718,112.34522)
    -->
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   id="path10"
   style="fill:#000000;stroke-width:2.42212"
   sodipodi0:nodetypes="ccc"
   d="M 266.26225,125.36729 L 230.64920,160.98034 L 217.62718,112.34522 Z" />
       
    <!-- Path12
         Original (relative path):
         A = (194.17326,201.33011), B = (163.34463,232.15873), Apex = (147.93027,185.91566)
         Centroid ≈ (168.48272,206.46817), v ≈ (–20.55245,–20.55251)
         New:
         p₁ ≈ (168.48272+28.08274, 206.46817–7.53031) = (196.56546,198.93786)
         p₂ ≈ (168.48272–7.53031, 206.46817+28.08274) = (160.95241,234.55091)
         p₃ = (147.93027,185.91566)
    -->
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   id="path12"
   style="fill:#000000;stroke-width:2.42212"
   sodipodi0:nodetypes="ccc"
   d="M 196.56546,198.93786 L 160.95241,234.55091 L 147.93027,185.91566 Z" />
       
    <!-- Path13
         Original: A = (194.17315,127.75956), B = (163.34452,158.58820), Apex = (147.93027,112.34513)
         Centroid ≈ (168.48265,132.89763), v ≈ (–20.55238,–20.55250)
         New:
         p₁ ≈ (168.48265+28.08274, 132.89763–7.53031) = (196.56539,125.36732)
         p₂ ≈ (168.48265–7.53031, 132.89763+28.08274) = (160.95234,160.98037)
         p₃ = (147.93027,112.34513)
    -->
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