Question

Find point P which internally divides the points A (-2,1) and B (1,4) in the ratio 2:1 .​

Answer 1

Step-by-step explanation:

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Using the section formula, if a point (x,y) divides the line joining the points (x 1 ,y 1 ) and (x 2) ,y 2 ) in the ratio m:n, then

(x,y)=( m+nmx 2+nx 1m+nmy +ny )

Let the co-ordinates of P(x,y) divides AB in the ratio m:n.

A(−2,1) and B(1,4) are the given points.

Given m:n=2:1

∴x 1

=−2,y 1

=1,x 2

=1,y 2

=4,m=2 and n=1

∴ By Section formula

x=(2×1+1×−2)/(2+1)

∴x=(2−2)/3

∴x=0/3

∴x=0

And

y=(2×4+1×1)/(2+1)

∴y=(8+1)/3

∴y=9/3

∴y=3

Hence the co-ordinate of point P are (0,3)

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Answer 2

Solution :-

Here , Point P which internally divides the point A and Point B in the ratio 2 : 1

The coordinates of point A = ( -2 , 1 )

The coordinates of point B = ( 1 , 4 )

Compare the coordinates with ( x1, y1 ) and( x2,y2) and Ratios with m1 and m2

Now,

By using section formulas

x = ( m1x2 + m2x1 / m1 + m2 )

y = ( m1y2 + m2y1/ m1 + m2 )

Here,

x1 and y1 are -2 and 1

x2 and y2 are 1 and 4

m1 and m2 are 2 and 1

Put the required values in the given formulas,

Therefore,

x = ( 2 * 1 + 1 * -2 / 2 + 1 )

x = ( 2 - 2 / 3 )

x = 0/3

x = 0

The value of x = 0

Now,

y = ( 2 * 4 + 1 * 1 / 2 + 1 )

y = ( 8 + 1 / 3 )

y = 9/3

y = 3

The value of y = 3

Hence, The coordinates of point P is ( 0,3 )$.$