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.
Answers
Step-by-step explanation:
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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} )