Let A be the point of intersection of the lines $3 \mathrm{x}+2 y=14,5 x-y=6$ and $B$ be the point of intersection of the lines $4 x+3 y=8,6 x+y=5$. The distance of the point $\mathrm{P}(5,-2)$ from the line AB is
Select the correct option:
A
$\frac{13}{2}$
B
8
C
$\frac{5}{2}$
D
6
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
Sol. Solving lines $\mathrm{L}_1(3 x+2 y=14)$ and $\mathrm{L}_2(5 x-y=6)$ to get $\mathrm{A}(2,4)$ and solving lines $\mathrm{L}_3(4 x+3 y=8)$ and $\mathrm{L}_4(6 \mathrm{x}+\mathrm{y}=5)$ to get $\mathrm{B}\left(\frac{1}{2}, 2\right)$.
Finding Eqn. of $\mathrm{AB}: 4 \mathrm{x}-3 \mathrm{y}+4=0$
Calculate distance PM
$$
\Rightarrow\left|\frac{4(5)-3(-2)+4}{5}\right|=6
$$
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