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Question

Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.


A

(6a+1a+1,8a+4a+1)

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B

(6a+2a+1,8a+4a+1)

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C

(6+2aa+1,8+4aa+1)

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D

(6a+8a+1,2a+4a+1)

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Solution

The correct option is B

(6a+2a+1,8a+4a+1)


The point, say P(x, y), divides the line AB into the ratio a : 1. The formula 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 AB
Applying the formula, we get ((1×2+a×6)a+1,1×4+a×8a+1)=(6a+2a+1,8a+4a+1)


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