Question

A(15,5), B(9,20) and A-P-B. find the ratio in which P(11,15)divides segment AB.

Answer 1

Hey friend, Here is your answer -
Here point P divide the line AB in the ratio m:n

Let The co-ordinates of point A are (x1 , y1) and point B are (x2,y2) ,point P are (x,y)

by using section formula,
x=mx2+nx1/m+n
11=m×9+n×15/m+n
11=9m+15n/m+n
11m+11n=9m+15n
2m=4n
m/n=4/2
m:n=2:1
The ratio in which P divides the AB is 2:1

Hope it will help you friend.

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Answer 2

Answer:

The ratio in which P(11,15)divides segment AB is 2:1.

Step-by-step explanation:

Given :

• A(15,5)
• B(9,20)
• A-P-B.

A point on the line segment divides it into two parts which may equal or not.

• The ratio in which the point divides the given line segment can be found if we know the coordinates of that point.
• Also, it is possible to find the point of division if we know the ratio in which the line segment joining two points has given.
• These two things can be achieved with the help of a section formula in coordinate geometry.

Section formula is used to determine the coordinate of a point that divides a line segment joining two points into two parts such that the ratio of their length is m:n.

Let P and Q be the given two points (x1,y1) and (x2,y2) respectively, and M be the point dividing the line-segment PQ internally in the ratio m:n, then form the sectional formula for determining the coordinate of a point M is given by:

P(x, y) = (mx2+nx1/m+n , my2+ny1/m+n)

To find :

The ratio in which P(11,15)divides segment AB.

by the formula:

$11= 9m+15n/m+n\\11m+11n=9m+15n\\2m=4n\\m/n=4/2 \\m/n=2/1$

hence ,

The ratio in which P(11,15)divides segment AB is 2:1.

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