Statement A (Assertion): The co-ordinates of the points which div… - Vidyadip

MCQ

Statement A (Assertion): The co-ordinates of the points which divides the line segment joining $A(2,-8)$ and $B(-3,-7)$ into three equal parts are $\left(\frac{1}{3},-\frac{23}{3}\right)$ and $\left(-\frac{4}{3},-\frac{22}{3}\right)$.
Statement R (Reason) : The points which divide $A B$ in the ratio $1: 3$ and $3: 1$ are called points of trisection of $A B$.

A
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is the correct explanation of assertion $(A)$.
B
Both assertion (A) and reason ( $R$ ) are true and reason $(R)$ is not the correct explanation of assertion (A).
C
Assertion $(A)$ is true but reason $(R)$ is false.
D
Assertion (A) is false but reason $(R)$ is true.

✓

Answer

(c) : Let $P$ and $Q$ be the points which divides $A(2,-8)$ and $B(-3,-7)$ into three equal parts.

$\therefore \quad A P: P B=1: 2$
So, coordinates of $p=\left(\frac{-3+4}{3}, \frac{-7-16}{3}\right)=\left(\frac{1}{3},-\frac{23}{3}\right)$
Also, $A Q: Q B=2: 1$
$\therefore \quad$ Coordinates of $Q=\left(\frac{-6+2}{3}, \frac{-14-8}{3}\right)$
$
=\left(-\frac{4}{3},-\frac{22}{3}\right)
$So, assertion is true but reason is false.

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