Another q on straight line...?

Question

A line y = kx cuts the line x + y = -2 at R and the line 2x + y = 5 at S. If the mid point of RS is the origin, O, find the coordinates of R and S. Find the point of intersection between the lines x + y = -2 and 2x + y =5.

Answer 1

Find the intersection points of y = kx with each of the lines.

For x + y = -2:

x + kx = -2 ..... x(k + 1) = -2 so x = -2/(k + 1) and y = -2k/(k + 1)

For 2x + y = 5:

2x + kx = 5 .... x(k + 2) = 5 so x = 5/(k + 2) and y =5k/(k + 2)

Since the origin is the midpoint, x from one should be -x from the other and the same for y. S:

-2/(k + 1) = -5/(k + 2) ....-2(k + 2) = -5(k + 1)

-2k - 4 = -5k - 5 ..... 3k = -1 and k = -1/3

For R:

x + (-1/3)x = -2

3x - x = -6

2x = -6

x = -3 and y = 1

For S:

2x + (-1/3)x = 5

6x - x = 15

x = 3 and y = -1

So the points are: R = (-3,1) and S = (3,-1)

Intersection of the two original lines:

y = -2 - x

2x + (-2 - x) = 5

x - 2 = 5

x = 7 and y = -9

Intersetion point is (7,-9)

Answer 2

Look at my source.  It might help.  I'm sure it will.  Just check it.  

Answer 3

O is the midpoint of RS means the coordinates of R and S are opposite of each other.

Now R = (-2/k(k+1), - 2/(1+k))

        S = ( 5/k(k+1), 5/(k+1))

But they are not opposit of each other. Check the Q again.

"Find the point of intersection between the lines x + y = -2 and 2x + y =5." is also not correct. How can the point of intersection be BETWEEN them? it must be on BOTH in fact.