Question

If the ratio in which f (x,y)
coordinates of the point P.
divides
the AB is k:1, then find coordinate of oint p​

Answer 1

you didn't mention about points A and B. without these we can't get the coordinate of point P.

ok, let A (x1 , y1) and B (x2 , y2)

a/c to question,

(x , y) is the coordinate of point P which divides the line AB in the ratio of k : 1

from section formula, we know, if two points (x1, y1) and (x2, y2) are divided into m : n ratio by a point (x, y) then,

$(x,y)=\left(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n}\right)$

so, x = (kx2 + x1)/(k + 1)

and y = (ky2 + y1)/(k + 1)

hence, coordinate of point P [(kx2 + x1)/(k + 1), (ky2 + y1)/(k + 1) ]

Answer 2

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= $\dfrac{(k.c+ a)}{(k+1)}$

y=$\dfrac{(k.d+ b)} {(k+1)}$

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