Question

The point P which divides the line segment joining the points A(2, -5) and B(5, 2) in the ratio 2 : 3 lies in the quadrant.

A. I
B. II
C. III
D. IV

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Answer 1

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⇒D

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If P(x, y) is the dividing point of the line joining AB then By Section Formula we have,

⇒X

$= \frac{mx2 + nx1}{m + n}$

⇒Y

$= \frac{my2 + ny1}{m + n}$

Where m and n is the ratio in which the point C divides the line AB.

Finding the x-coordinate of P:

⇒x= 2×2+3×2/2+3

⇒x= 10+6/5

⇒x=16/3

Finding the y-coordinate of P:

⇒y=2×2+3×(-5)/2+3

⇒y=4-15/5

⇒y= -11/3

Therefore the coordinates of P is (16/3, -11/3).

Since in fourth quadrant x-coordinate is positive and y-coordinate is negative.

Therefore the point P lies in the fourth quadrant.