There is a triangle ABC: A (-2,3), B (4, -1), C (2,5). Determine the general equations of the lines on which they lie:
a) AB side,
b) height to side c,
c) Axis of the AB side,
d) median ta to side a

Correct answer:

p1 = p1
p2 = p2
p3 = p3
p4 = p4

Step-by-step explanation:

a0=2;a1=3 b0=4;b1=1 c0=2;c1=5  p1:ax+by+c=0 c=10  a a0+b a110=0 a b0+b b110=0 a (2)+b 310=0 a 4+b (1)10=0  2a3b=10 4ab=10  Pivot:Row1Row2 4ab=10 2a3b=10  Row242 Row1Row2 4ab=10 2.5b=15  b=2.515=6 a=410+b=410+6=4  a=4 b=6  p1: 6x+4y10=0  p1
p2 p1; C  p2  n2 = (b;a)  p2:n0 x+n1 y+z=0  b c0+a c1+z=0 6 2+4 5+z=0  z=8  z=18=8  z=8  p2: 6x+4y8=0 p2: 6x4y+8=0  p2
S = AB/2 s0=(a0+b0)/2=((2)+4)/2=1 s1=(a1+b1)/2=(3+(1))/2=1  p3:n0 x+n1 y+w=0  b s0+a s1+w=0 6 1+4 1+w=0  w=2  w=12=2  w=2  p3: 6x+4y+2=0 p3: 6x4y2=0  p3
p4 = CS  v0 c0+v1 c13=0 v0 s0+v1 s13=0 v0 2+v1 53=0 v0 1+v1 13=0  2v0+5v1=3 v0+v1=3  Row221 Row1Row2 2v0+5v1=3 1.5v1=1.5  v1=1.51.5=1 v0=235v1=235 (1)=4  v0=4 v1=1  p4:4xy3=0 p4

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