Question

the ratio in which p(x,y) divides the AB is k:1 then find coordinates of the point p​

Answer 1

Answer:

In general if the coordinates of A and B is given we can  proceed with section formula to find the coordinates of p, as the coordinates of A and B is not given, let us take the coordinate of A(a,b) and B(c,d)

By applying section formula:

x= (k.c+ a)÷(k+1)

y= (k.d+ b)÷(k+1)

If the numerical values of the coordinates is given , the numerical values of the coordinates of A and B can be obtained.

Answer 2

Answer:

$(\frac{kc+a}{k+1},\frac{kd+b}{k+1})$

Step-by-step explanation:

Let us assume that the coordinates of points A & B are (a,b) and (c,d) respectively.

Now given that point P(x,y) divides the line AB in k:1 ratio.

We have to find the coordinates of P(x,y) in terms of a,b,c,d, and k.

We have the formula, if a point Z divides the straight line PQ, where coordinate of P and Q are  P(p,q) and Q(r,s) in the ratio of m:n, then co-ordinates of Z will be given by, $(\frac{mr+np}{m+n},\frac{ms+nq}{m+n})$.  

Therefore, the co-ordinates of P are given by  

P(x,y)≡ $P(\frac{kc+a}{k+1},\frac{kd+b}{k+1})$

This is the answer.