1. ## Line problems.

Hey guys,

I need help to solve the following problems:

1) The line y - 2x + 3 = 0 intersects the curve y = x^2 - 2x at the point A and B. Find the co-ordinates of A and B.

2) Determine whether the points A(-4, 3) B(-1, 5) and C(8, 11) are collinear.

(In this question what does it mean by collinear?)

Lastly..

3) Find the point at which the line with the equation 3y - 12 = 4x cuts (i) the y-axis and (ii) the x-axis.

Hey guys,

I need help to solve the following problems:

1) The line y - 2x + 3 = 0 intersects the curve y = x^2 - 2x at the point A and B. Find the co-ordinates of A and B.
2) Determine whether the points A(-4, 3) B(-1, 5) and C(8, 11) are collinear.
(In this question what does it mean by collinear?)
Lastly..
3) Find the point at which the line with the equation 3y - 12 = 4x cuts (i) the y-axis and (ii) the x-axis.
Hello,

to 1): Transform the equation of the line to y = 2x-3. In the intersecting points the y-values of the line and the parabola must be equal:
Solve 2x-3=x^2-2x.
x^2-4x+3=0 ----> x = 3 or x = 1. Plug in these values into the equation of the line and you'll get: A(3,3) and B(1,-1).

to 2)
"collinear" means: forming a line. With 2 points, using the 2-point-formula of the line, you'll get an equation. Plug in the coordinates of the 3rd point and look if they fit into the equation:
$\displaystyle \frac{y-5}{x-(-1)}=\frac{3-5}{-4-(-1)} \Leftrightarrow y=\frac{2}{3} x+\frac{17}{3}$
Plug in the coordinates of C: $\displaystyle 11=\frac{2}{3} 8+\frac{17}{3}$
$\displaystyle 11 = \frac{33}{3}\rightarrow C\in \mbox{line}$

to 3)
(i): x = 0 ----> y = 4, so S(0 , 4)
(ii): y = 0 ----> x = -3, so Z(-3 , 0)

Greetings

EB

3. Thanks

Could not have been explained any better!

Kind Regards,