Question 1119234
A) find the equation of the line through the points A (0,4) and B (3,2)
<pre>
Here's the picture:

{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7), line(-9,10,9,-2),circle(0,4,.1), circle(3,2,.1),
locate(.3,4.3,"A(0,4)"), locate(3.3,2.3,"B(3,2)") )}}}{{{matrix(11,1,
m=(y[2]-y[1])/(x[2]-x[1]),
m=(2-4)/(3-0),
m=(-2)/3,
m=-2/3,
y-y[1]=m*(x-x[1]),
y-4=expr(-2/3)(x-0),
y-4=expr(-2/3)x,
y=expr(-2/3)x+4,
OR,
3y=-2x+12,
2x+3y=12)}}}
</pre>
B) find l, the equation of the line through B and is perpendicular to AB
<pre>
{{{matrix(12,1,
m=(y[2]-y[1])/(x[2]-x[1]),
m=3/2,
y-y[1]=m*(x-x[1]),
y-2=expr(3/2)*(x-3),
y-2=expr(3/2)*x-9/2,
y=expr(3/2)x-9/2+2,
y=expr(3/2)x-9/2+4/2,
y=expr(3/2)x-5/2,
OR,
2y=3x-5,
-3x+2y=-5,
3x-2y=5
)}}}
Here's the picture:

{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7), line(-9,10,9,-2),circle(0,4,.1), circle(3,2,.1), line(-7,-13,7,8),
locate(.3,4.3,"A(0,4)"), locate(3.3,2.3,"B(3,2)") )}}}
</pre>
C) the line l intersects the y axis at C. 
<pre>
Find the coordinates of C by setting x = 0 in line 1
{{{matrix(1,5,
3x-2y=5,
3(0)-2y=5,
0-2y=5,
-2y=5,
y=-5/2)}}} 
So the point is C(0,-5/2)

{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7), line(-9,10,9,-2),circle(0,4,.1), circle(3,2,.1), circle(0,-5/2,.1),
locate(0.3,-5/2+.3,"C(0,-5/2)"),

line(-7,-13,7,8),
locate(.3,4.3,"A(0,4)"), locate(3.3,2.3,"B(3,2)") )}}}
</pre>
Find the area of triangle ABC:
<pre>
It's the absolute value of this determinant:
{{{A=expr(1/2)abs(matrix(3,3,0,4,1,3,2,1,0,-5/2,1))=expr(1/2)abs(-39/2)=39/4}}}

Edwin</pre>