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Question

In the figure, line segment AB meets x - axis at A and y - axis at B. The point P(-3, 4) on AB divides it in the ratio 2 : 3.
The coordinates of A and B respectively are ________ .


A
(-10, 0) and (0, 10)
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B
(-5, 0) and (0, 5)
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C
(-5, 0) and (0, 10)
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D
(-10, 0) and (0, 10)
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Solution

The correct option is C (-5, 0) and (0, 10)

Given:
'A' is a point on X-axis and 'B' is a point on Y axis.
Hence, let the coordinates of A be (x, 0) and of B be (0, y).

Point P(-3, 4) divides the line segment AB in the ratio 2 : 3.

We know that the coordinates of the point P that divides a line segment in the ratio m : n is given by

P(x,y)=(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.
Then,
3=m(0)+n(x)m+n
3m3n=nx
3(2)3(3)=3(x)
15=3xx=5

Also, 4=(2)(y)+(3)(0)2+3
20=2yy=10

Coordinates of A is (-5, 0) and that of B is (0, 10).


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