State whether the following statement is true | vedclass

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

Question

(A) True.Let point $P(5, -3)$ divide the line segment joining $A(7, -2)$ and $B(1, -5)$ in the ratio $k: 1$ internally.By the section formula,the coor

Vedclass · Accepted Answer

True

Vedclass · Answer

(A) True.Let point $P(5, -3)$ divide the line segment joining $A(7, -2)$ and $B(1, -5)$ in the ratio $k: 1$ internally.By the section formula,the coordinates of point $P$ are given by:$\left( \frac{k(1) + 1(7)}{k + 1}, \frac{k(-5) + 1(-2)}{k + 1} \right) = \left( \frac{k + 7}{k + 1}, \frac{-5k - 2}{k + 1} \right)$.Equating these to the given coordinates of $P(5, -3)$:$\frac{k + 7}{k + 1} = 5 \implies k + 7 = 5k + 5 \implies 2 = 4k \implies k = \frac{1}{2}$.Checking the $y$-coordinate with $k = \frac{1}{2}$:$\frac{-5(1/2) - 2}{1/2 + 1} = \frac{-2.5 - 2}{1.5} = \frac{-4.5}{1.5} = -3$.Since the ratio is $1: 2$,point $P$ divides the segment $AB$ such that it is one of the two points of trisection (the other being at ratio $2: 1$). Thus,the statement is true.

State whether the following statement is true or false. Justify your answer.
Point $P(5, -3)$ is one of the two points of trisection of the line segment joining the points $A(7, -2)$ and $B(1, -5)$.

Similar Questions

If the distance between the points $(4, p)$ and $(1, 0)$ is $5,$ then the value of $p$ is

Find the values of $k$ if the points $A(k+1, 2k)$,$B(3k, 2k+3)$ and $C(5k-1, 5k)$ are collinear.

The distance between $(7, 5)$ and $(2, 5)$ is........

When point $A(x_{1}, y_{1})$ and point $B(x_{2}, y_{2})$ are joined to form $\overline{AB}$ and a point divides $\overline{AB}$ in the ratio $\lambda : 1$,the coordinates of the point are:

Prove that the points $A(1, 1)$,$B(4, 4)$,and $C(6, 2)$ are the vertices of a right-angled triangle.

Vedclass Test Series

Exam Paper Generator

Online Exam Module

State whether the following statement is true or false. Justify your answer.Point $P(5, -3)$ is one of the two points of trisection of the line segment joining the points $A(7, -2)$ and $B(1, -5)$.