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)
• B. (-5, 0) and (0, 5)
• C. (-5, 0) and (0, 10)
• D. (-10, 0) and (0, 10)

Answer 1

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

$P(x,y)=(\frac{n\times x_1+m\times x_2}{m+n},\frac{n\times y_1+m\times y_2}{m+n})$

where, $(x_1,y_1)and(x_2,y_2)$ are the coordinates of the endpoints of the line segment.
Then,
$-3=\frac{m\left(0\right)+n\left(x\right)}{m+n}$
$\Rightarrow -3m-3n=nx$
$\Rightarrow -3\left(2\right)-3\left(3\right)=3\left(x\right)$
$\Rightarrow -15=3x\Rightarrow x=-5$

Also, $4=\frac{\left(2\right)\left(y\right)+\left(3\right)\left(0\right)}{2+3}$
$\Rightarrow 20=2y\Rightarrow y=10$

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