Determine the ratio in which the line 2x+y−4=0 divides the line segment joining the points A(2, -2) and B (3, 7).
2 : 9
9 : 2
9 : 1
1 : 9
2 : 9
Let the required ratio be k : 1 and let point C divide them in the above ratio.
We know that the coordinates of the point that divides a line segment in the ratio m : n is given by
where (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line segment.
∴ Coordinates of C are (3k+2k+1,7k−2k+1)
Since point C lies on the line represented by the equation
2x+y−4=0, it will satisfy the equation.
∴ So we have
∴ The required ratio is k : 1= 2 : 9.