First slide

Cartesian plane

Question

In a $Δ P Q R, I$ is the in-centre and $\overset{\leftrightarrow}{P I}$ cuts $\bar{Q R}$ at $S$ . If $Q = (- 1, 2), R = (9, 7), P Q = 14, P R = 21$ then $S$ is

Difficult

A

$(5, 5)$
B

$(4, \frac{9}{2})$
C

$(- \frac{21}{5}, - \frac{8}{5})$
D

$(3, 4)$

Solution

$Q (- 1, 2), R (9, 7)$
$Q R \sqrt{100 + 25} = 25$

$P I$ cuts $\bar{Q R}$ at $' s'$

In the ratio $P Q : P R = 14 : 21 = 2 : 3$

$S = \frac{2 R + 3 Q}{2 + 3} = \frac{(18, 14) + (- 3, 6)}{5} = (3, 4)$

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