The coordinates of the points A, B, C are (x_ | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The coordinates of $D$ which divides $AB$ in the ratio $l : k$ are given by the section formula:$D = \left( \frac{l x_2 + k x_1}{l + k}, \frac{l y

Vedclass · Accepted Answer

$\left( \frac{k x_1 + l x_2 + m x_3}{k + l + m}, \frac{k y_1 + l y_2 + m y_3}{k + l + m} \right)$

Vedclass · Answer

(A) The coordinates of $D$ which divides $AB$ in the ratio $l : k$ are given by the section formula:$D = \left( \frac{l x_2 + k x_1}{l + k}, \frac{l y_2 + k y_1}{l + k} \right)$Now,$P$ divides the line segment $DC$ in the ratio $m : (k + l)$.Using the section formula for $P$ with $D = (x_D, y_D)$ and $C = (x_3, y_3)$:$P = \left( \frac{m x_3 + (k + l) x_D}{m + k + l}, \frac{m y_3 + (k + l) y_D}{m + k + l} \right)$Substituting the coordinates of $D$:$x_P = \frac{m x_3 + (k + l) \left( \frac{l x_2 + k x_1}{l + k} \right)}{k + l + m} = \frac{m x_3 + l x_2 + k x_1}{k + l + m}$Similarly,$y_P = \frac{m y_3 + l y_2 + k y_1}{k + l + m}$Thus,the coordinates of $P$ are $\left( \frac{k x_1 + l x_2 + m x_3}{k + l + m}, \frac{k y_1 + l y_2 + m y_3}{k + l + m} \right)$.

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

Similar Questions

If the portion of a straight line intercepted between the coordinate axes is divided by the point $(2,3)$ in the ratio $2:3$,then the product of the intercepts made by this line on the axes is

The straight line $3x + y = 9$ divides the line segment joining the points $(1, 3)$ and $(2, 7)$ in the ratio

If the points $A(6, -1)$,$B(1, 3)$ and $C(x, 8)$ are such that $AB = BC$,then $x = $

Find the distance of the point $P(-8, 6)$ from the origin.

If $C$ is the reflection of $A(2, 4)$ in the $x$-axis and $B$ is the reflection of $C$ in the $y$-axis, then $|AB|$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module