Question

the point of A (-1,-7) and B(4,-3) and of the line AB-point P divides in Ratio 2:3 find the coordinate of point P.​

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

Given :-

The point of A (-1,-7) and B(4,-3) and of the line AB-point P divides in Ratio 2:3

To find :-

Find the coordinate of point P?

Solution :-

Given points are : A (-1,-7) and B(4,-3)

Let (x1, y1) = A(-1,-7) => x1 = -1 and y1 = -7

Let (x2, y2) = B(4,-3) => x2 = 4 and y2 = -3

Given ratio = 2:3

Let m1:m2 = 2:3 => m1 = 2 and m2 = 3

We know that

The coordinates of a point P(x,y) which divides the linesegment joining the points (x1, y1) and

(x2, y2) in the ratio m1:m2 is P(x,y) =

( { m1x2+m2x1}/{m1+m2},{m1y2+m2y1}/{m1+m2} )

On Substituting these values in the above formula then

=> P(x,y)

=> ( {2×4+3×-1}/{2+3},{2×-3+3×-7}/{2+3} )

=> ( { 8+(-3)} /5 , { -6+(-21) }/5 )

=> ( { 8-3)/5 , { -6-21}/5 )

=> ( 5/5 , -27/5 )

=> ( 1, -27/5)

Therefore , P(x,y) = ( 1, -27/5 )

Answer:-

The coordinates of the point P(x,y) for the given problem is (1,-27/5)

Used formulae :-

Section formula :-

The coordinates of a point P(x,y) which divides the linesegment joining the points (x1, y1) and

(x2, y2) in the ratio m1:m2 is P(x,y) =

( { m1x2+m2x1}/{m1+m2},{m1y2+m2y1}/{m1+m2} )