Question

# 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

Solution

## The correct option is A 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 (n×x1+m×x2m+n,n×y1+m×y2m+n) 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 2(3k+2k+1)+(7k−2k+1)−4=0 ⇒2(3k+2)+(7k−2)=4×(k+1) ⇒6k+4+7k−2−4k−4=0 ⇒9k−2=0 ⇒k=29 ∴ The required ratio is k : 1= 2 : 9.

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