Step 1
Find the slope of the line AB
Let
[tex]A(-4,0)\ B(2,-3)[/tex]
we know that
The slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-3-0}{2+4}[/tex]
[tex]m=\frac{-3}{6}[/tex]
[tex]m=-\frac{1}{2}[/tex]
Step 2
Find the equation of the line
we know that
If two lines are parallel, then their slopes are the same
so
[tex]m1=m2[/tex]
The equation of the line into slope-point form is equal to
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{1}{2}[/tex]
point [tex]C(-2,2)[/tex]
substitute
[tex]y-2=-\frac{1}{2}(x+2)[/tex]
[tex]y=-\frac{1}{2}x+1[/tex]
Step 3
Find the point on the x-axis that lies on the line
the equation of the line is [tex]y=-\frac{1}{2}x+1[/tex]
we know that
if the point lies on the x-axis
then
the y-coordinate of the point is equal to zero
so
For [tex]y=0[/tex]
find the x-value
[tex]0=-\frac{1}{2}x+1[/tex]
[tex]\frac{1}{2}x=1[/tex]
[tex]x=2[/tex]
therefore
the answer is
the point is [tex](2,0)[/tex]
