I tried the code below (I sort of translated it from written notation), where I hoped that [Intersection] would give me the intersection of line ac with the altitude from b:

scene1 = 
  GeometricScene[{a, b, c, d}, 
    {Triangle[{a, b, c}], 
    d ∈ {Line[{a, c}] ⋂ 
      TriangleConstruct[{a, b, c}, "Altitude"]}, 
      TriangleConstruct[{a, c, b}, "Altitude"]}];
RandomInstance[scene1, 3]

It did not work. How do I then define the intersection of two lines as a point?


1 Answer 1


If you want to get the intersection of two line, it is recommend that use {Line[{a,x,c}],Line[{b,x,d}]} or {InfiniteLine[{a, x, c}], InfiniteLine[{b, x, d}]} etc.

 GeometricScene[{a, b, c, d, x}, {InfiniteLine[{a, x, c}], 
   InfiniteLine[{b, x, d}]}]

If you want to get the Foot of Altitude,maybe you can try the following approach.

GeometricScene[{a, b, c, 
   d -> TriangleConstruct[{a, b, c}, {"Foot", b}]}, {Line[{a, c}], 
   Line[{b, d}]}]~RandomInstance~3

enter image description here

  • $\begingroup$ What is ~ supposed to mean and how is it used? It only says 'Infix' in the Wolfram Documentation. $\endgroup$
    – Cheng
    Commented Sep 23, 2020 at 12:40
  • 1
    $\begingroup$ @Cheng a~f~b just as f[a,b] $\endgroup$
    – cvgmt
    Commented Sep 23, 2020 at 12:52

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