Straight Lines Question 9
Question 9 - 2024 (29 Jan Shift 2)
Let $A$ be the point of intersection of the lines $3 x+2 y=14,5 x-y=6$ and $B$ be the point of intersection of the lines $4 x+3 y=8,6 x+y=5$. The distance of the point $P(5,-2)$ from the line $A B$ is
(1) $\frac{13}{2}$
(2) 8
(3) $\frac{5}{2}$
(4) 6
Show Answer
Answer (4)
Solution
Solving lines $\mathrm{L}{1}(3 \mathrm{x}+2 \mathrm{y}=14)$ and $\mathrm{L}{2}(5 \mathrm{x}-\mathrm{y}=6)$ to get $\mathrm{A}(2,4)$ and solving lines $\mathrm{L}{3}(4 \mathrm{x}+3 \mathrm{y}=8)$ and $L{4}(6 x+y=5)$ to get $B\left(\frac{1}{2}, 2\right)$.
Finding Eqn. of $\mathrm{AB}: 4 \mathrm{x}-3 \mathrm{y}+4=0$
Calculate distance PM
$\Rightarrow\left|\frac{4(5)-3(-2)+4}{5}\right|=6$
