Question

The coordinates of the points A, B, C are $(x_{1},y_{1})$, $(x_{2},y_{2})$, $(x_{3},y_{3})$ and D divides the line AB in the ratio l : k. If P divides the line DC in the ratio m : k + l, then the coordinates of P are.

• A. $\left( \frac{kx_{1} + lx_{2} + mx_{3}}{k + l + m},\frac{ky_{1} + ly_{2} + my_{3}}{k + l + m} \right)$
• B. $\left( \frac{lx_{1} + mx_{2} + kx_{3}}{l + m + k},\frac{ly_{1} + my_{2} + ky_{3}}{l + m + k} \right)$
• C. $\left( \frac{mx_{1} + kx_{2} + lx_{3}}{m + k + l},\frac{my_{1} + ky_{2} + ly_{3}}{m + k + l} \right)$
• D. None of these

Answer 1

Answer: (A)

$\left( \frac{kx_{1} + lx_{2} + mx_{3}}{k + l + m},\frac{ky_{1} + ly_{2} + my_{3}}{k + l + m} \right)$

Answer 2

Coordinates of D will be $\left( \frac { l x _ { 2 } + k x _ { 1 } } { l + k } , \frac { l y _ { 2 } + k y _ { 1 } } { l + k } \right)$

Now again, DC is divided by P in

Then the coordinates of P will be given by

$\left( \frac { m x _ { 3 } + l x _ { 2 } + k x _ { 1 } } { k + l + m } , \frac { m y _ { 3 } + l y _ { 2 } + k y _ { 1 } } { k + l + m } \right)$.