First slide

Cartesian plane

Question

$P = (- 5, 4) and Q = (- 2, - 3)$ . If $\bar{P Q}$ is produced to $R$ such that p divides $\bar{Q R}$ externally in the ratio $1 : 2$ , then $R$ is

Easy

A

$(1, 10)$
B

$(1, - 10)$
C

$(10, 1)$
D

$(2, - 10)$

Solution

P divides $Q R$ in the ratio $1 : 2$ externally
$\Rightarrow P Q : P R = 1 : 2 \Rightarrow 2 P Q = P R$

$\Rightarrow Q$ is the midpoint of $P R \Rightarrow R = 2 Q - P = (1, - 10)$

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