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Question

A(2, 4) and B(8, 12) are two ends of a line segment. Find the point which divides AB internally in the ratio 1:3.


A

(3.75, 5)

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B

(3, 6.5)

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C

(3.5, 6)

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D

(3, 6)

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Solution

The correct option is C

(3.5, 6)


Let the point P(x,y) divide AB in the ratio 1:3.

The coordinates of the point that divides a line segment internally , joining the points (x1,y1) and (x2,y2) in the ratio m : n are:

(n×x1+m×x2m+n,n×y1+m×y2m+n)

Here,
x1=2, y1=4x2=8, y2=12m=1, n=3

So, (x,y)=(1×8+3×21+3, 1×12+3×41+3)
=(144, 244) =(72, 6)

The point that divides AB in the ratio 1:3 is (72, 6).


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