Question

The line x+y=10 divides line segment AB in the ratio a:1. Find the value of a. 2 12 1 3

Solution

The correct option is C 1 The point, say P(x,y), divides the line AB into the ratio a:1. The equation for the point that divides a line in the ratio m : n is, ((n×x1+m×x2)m+n,n×y1+m×y2m+n) Where (x1,y1) and (x2,y2) are the coordinates of the endpoints of the line segment. Applying the formula, we get (1×2+a×6)a+1,1×4+a×8a+1) This point lies on the line x+y=10, so substitute the points in the equation for the line. (1×2+a×6)a+1+1×4+a×8a+1=106a+2+8a+4=10(a+1)⇒4a=4⇒a=1

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