Question

The co-ordinates of points A, B, C are (x1, yı) (x2, y2) and (x3, y3) and point D d
AB in the ratio l: k. if p divides line DC in the ratio m : (k +l ) then the co-ordinates
of P are​

Answer 1

$\textbf{Section formula:}$

$\text{The co ordinates of the point which divides the}$

$\text{line segment joining (x_1,y_1) and (x_2,y_2) internally in the ratio m:n are}$

$\boxed{\bf(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})}$

$\textbf{Given:}$

$A(x_1,y_1),\;B(x_2,y_2)\;\text{and}\;C(x_3,y_3)$

$\text{Since D divides AB internally in the ratio l:k,}$

$\text{the coordinates of D are}$

$(\dfrac{lx_2+kx_1}{l+k},\dfrac{ly_2+ky_1}{l+k})$

$\text{Since P divides DC internally in the ratio m : k+l,}$

$\text{the coordinates of P are}$

$(\dfrac{mx_3+(k+l)\frac{(lx_2+kx_1}{l+k})}{m+k+l},\dfrac{my_3+(k+l)\frac{(ly_2+ky_1}{l+k})}{m+k+l})$

$(\dfrac{mx_3+lx_2+kx_1}{m+k+l},\dfrac{my_3+ly_2+ky_1}{m+k+l})$

$\bf(\dfrac{kx_1+lx_2+mx_3}{k+l+m},\dfrac{ky_1+ly_2+my_3}{k+l+m})$

$\textbf{Answer:}$

$\textbf{The co-ordinates of D are}$

$\bf(\dfrac{kx_1+lx_2+mx_3}{k+l+m},\dfrac{ky_1+ly_2+my_3}{k+l+m})$

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