Straight Lines
Trisection of Line Segment — Intersection
nta_pyq_2023_apr
Grade 11
Question:
Lines $l_1$ and $l_2$ through origin trisect the segment of $L:\ 9x+5y=45$ between axes. If $m_1,m_2$ are their slopes, the intersection of $y=(m_1+m_2)x$ with $L$ lies on
y-2x=5
6x+y=10
y-x=5
6x-y=15
Step-by-Step Solution
Key Concept: Trisection points of segment $A(5,0),B(0,9)$: $C=(\frac{10}{3},3)$ and $D=(\frac{5}{3},6)$. $m_1=\frac{9}{10}$, $m_2=\frac{18}{5}$. $m_1+m_2=\frac{9}{2}$.
Intersection: $(\frac{10}{7},\frac{45}{7})$. $y-x=5$.
Correct Answer: 3