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Question

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


A
137,207
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B
157,227
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C
(2, 3)
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D
(4,3)
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Solution

The correct option is A 137,207

Let the coordinates of the point which divides AB in the ratio 3:4 be (x, y).

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

(m×x2+n×x1m+n,m×y2+n×y1m+n)

By substituting the given values, we get

(x, y)=(3×3+4×13+4,3×4+4×23+4)

(x, y)=(137,207)

Coordinates of the point which divides (internally) the line segment AB in the ratio 3 : 4 are (137,207).


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