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Find the coordinates of x and y such that (x, y) divides line joining (7, 1) and (3-5) in the ratio of 2:1.​

Answer 1

Step-by-step explanation:

Given:-

Two points (7, 1) and (3-5)

To find:-

Find the coordinates of x and y such that (x, y) divides line joining (7, 1) and (3-5) in the ratio of 2:1.

Solution:-

Given points are (7, 1) and (3-5)

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

Let (x2, y2)=(3,-5)=>x2=3 and y2=-5

Given ratio = 2:1

m1:m2=2:1=>m1=2 and m2=1

We know that

The coordinates of the point P(x,y) which divides the points (x1,y1) and (x2,y2) joining the line segment in the ratio m1:m2 is

[(m1x2+m2x1)/(m1+m2),(m1y2+m2y1)/(m1+m2)]

On Substituting these values in the formula

[{(2)(3)+(1)(7)}/(2+1),{(2)(-5)+(1)(1)}/(2+1)]

=>[(6+7)/3,(-10+1)/3]

=>(13/3,(-9/3)

=>(13/3,-3)

P(x,y)=(13/3,-3)

Answer:-

The Coordinates of x and y such that divides the given line segment joining the given points in the ratio 2:1 is (13/3,-3)

Used formula:-

• The coordinates of the point P(x,y) which divides the points (x1,y1) and (x2,y2) joining the line segment in the ratio m1:m2 is

[(m1x2+m2x1)/(m1+m2),(m1y2+m2y1(m1+m2)]