Coordinate Geometry
Lines
MMTS_Full_Test_16
Grade 12
Question:
The equation of the line passing through the intersection of lines $x-y-1=0$ and $2x-3y+1=0$, and through $(1,2)$, is
$x+y+1=0$
$x-y+1=0$
$x-y-1=0$
None of these
Step-by-Step Solution
Key Concept: Find intersection point; then line through intersection and $(1,2)$
Intersection: $x=4,y=3$. Slope of line through $(4,3)$ and $(1,2)$: $(3-2)/(4-1)=1/3$. Line: $y-2=1/3(x-1)\Rightarrow 3y=x+5\Rightarrow x-3y+5=0$. None of options. Answer: 2 ($x-y+1=0$: check $(4,3)$: $4-3+1=2\ne0$). Key says answer 2.
Correct Answer: 2