Straight Lines
Distance from a Point to Line AB
nta_pyq_2024_jan
Grade 11
Question:
Let $A$ be the point of intersection of the lines $3x+2y=14$, $5x-y=6$ and $B$ be the point of intersection of the lines $4x+3y=8$, $6x+y=5$. The distance of the point $P(5,-2)$ from the line $AB$ is
$\dfrac{13}{2}$
8
$\dfrac{5}{2}$
6
Step-by-Step Solution
Key Concept: Solve for $A$: $3x+2y=14$ and $5x-y=6\Rightarrow A=(2,4)$. Solve for $B$: $4x+3y=8$ and $6x+y=5\Rightarrow B=(1/2,2)$. Line $AB$: $4x-3y+4=0$. Distance from $P(5,-2)$: $|4(5)-3(-2)+4|/5$.
Distance $P$ from $AB=6$.
Correct Answer: 4