Question

find the coordinates of the point which divides internally the line joining the points (p,q) and (q,p) in the ratio (p-q):(p+q)

Answer 1

$[\frac{p^{2} + 2pq - q^{2}}{2p}, \frac{p^{2} + q^{2}}{2p}]$

Step-by-step explanation:

The coordinates of the point P(h,k) which divides internally the line joining the points A(p,q) and B(q,p) in the ratio (p - q) : (p + q) will be

(h,k) ≡ $[\frac{p(p + q) + q(p - q)}{(p + q) + (p - q)}, \frac{q(p + q) + p(p - q)}{(p + q) + (p - q)} ]$

(h,k) ≡ $[\frac{p^{2} + 2pq - q^{2}}{2p}, \frac{p^{2} + q^{2}}{2p}]$ (Answer)

Note: The coordinates of a point (h,k) which divides internally the line joining the points $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio m : n will be given by the formula

(h,k) ≡ $[\frac{nx_1 + mx_2}{m + n}, \frac{ny_1 + my_2}{m + n}]$