Question

if the point (x, y) divides the line segment joining the point A(x1, y1) and B(x2, y2) in the ratio k:1 then write the coordinates of the point p​

Answer 1

Answer:

The coordinates P is given by

           P(x,y) =  [(kx₂+x₁)/(k+1) , (ky₂+y₁)/(k+1)]

Step-by-step explanation:

Section formula:

• If a line segment's coordinates are provided, we can use the section formula to locate the point that divides the given line segment into two parts that may or may not be equal. If the point's coordinates are provided, we can also use the section formula to locate the ratio in which the point divides the given line segment.
• The section formula is used to determine the coordinates of a point C when it splits a line segment AB in the ratio m:n.
• Two types of the section formula exist. These types are reliant on point C, which may lie outside the line segment or in between the points.

The two varieties are:

Internal Section formula and External Section formula

Internal Section formula:

• When the point divides the line segment in the ration m:n internally at point C then that point lies in between the coordinates of the line segment then we can use this formula. It is also called as Internal Division.

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

  Given points A(x₁,y₁) and B(x₂,y₂) are the two points joining the line

and the point P(x,y) divides the line segment in the ratio m:n = k:1 then the coordinates P is given by

           P(x,y) =  [(kx₂+x₁)/(k+1) , (ky₂+y₁)/(k+1)]

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Answer 2

Answer:

The coordinates of point P are

$P(x,y)=(\frac{kx_{2}+x_{1}}{k+1},\frac{ky_{2}+y_{1}}{k+1})$

Step-by-step explanation:

The given points are $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ and it is given that,

The point P(x,y) divides the line segment joining the above points in the ratio k:1.

From the section formula, we know that if P(x,y) divides the line segment joining $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ in the ratio $m:n$ then its coordinates are

$P(x,y)=(\frac{mx_{2}+nx_{1}}{m+n},\frac{my_{2}+ny_{1}}{m+n})$

For the given question $m=k,n=1$ and hence the required coordinates are

$P(x,y)=(\frac{kx_{2}+x_{1}}{k+1},\frac{ky_{2}+y_{1}}{k+1})$

Therefore,

The coordinates of point P are

$P(x,y)=(\frac{kx_{2}+x_{1}}{k+1},\frac{ky_{2}+y_{1}}{k+1})$

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