# How to define the intersection of two lines as a point

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?

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.

Clear["*"];
RandomInstance@
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


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