Question

The co-ordinates of the point Q(x,y) which divides the line segment joining A(−2,1) and B(1,4) in the ratio 2:1 are​

Answer 1

Step-by-step explanation:

Given :-

The points are A(−2,1) and B(1,4)

To find :-

Find the co-ordinates of the point Q(x,y) which divides the line segment joining A(−2,1) and B(1,4) in the ratio 2:1 ?

Solution :-

Given points are A(−2,1) and B(1,4)

Let (x1, y1) = (-2,1) => x1 = -2 and y1 = 1

Let (x2, y2) = (1,4) => x2 = 1 and y2 = 4

Given ratio = 2:1

Let m1:m2 = 2:1

=> m1 = 2 and m2 = 1

We know that

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

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

Now,

The co-ordinates of the point Q(x,y) which divides the line segment joining A(−2,1) and B(1,4) in the ratio 2:1

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

=>({2+(-2)}/3 , {8+1}/3)

=> ((2-2)/3,9/3)

=> (0/3,9/3)

=> (0,3)

Therefore, Q(x,y) = (0,3)

Answer :-

The coordinates of the point Q(x,y) = (0,3)

Used Formulae:-

Section formula:-

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

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

Points to know:-

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

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

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

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

→ Coordinate Geomerty was developed by Renes Descartes

Answer 2

Answer:

Using the section formula, if a point (x,y) divides the line joining the points

$(x1,y1) \: and \: (x2,y2) \: internally \: in \: the \: ratio \: m:n, \: then \: (x,y) \: =(m+nmx2+nx1,m+nmy2+ny1)$

$Substituting \: (x1,y1) \: =(−2,1) and \: (x2,y2)= \: (1,4) \: and \: m=2,n=1 \: in \: the \: section \: formula, \: we \: get \: the \: </p><p></p><p>point as \:$

$Q=(2+12(1) \: +1 \: (−2) \: ,2+12(4) \: +1(1)) \: =(32+(−2) \: ,38+1) \: =(0,3)$

Step-by-step explanation:

you can do it like this too mansi :)