Coordinate Geometry
Straight Lines
MMTS_Full_Test_20
Grade 12
Question:
Consider: I) General form $ax+by+c=0$ ($a,b,c\in\mathbb{R}$) always represents a straight line. II) A line $ax+by+1=0$ is such that algebraic sum of perpendiculars from $(x_i,y_i)$ $(i=1,2,\ldots,n)$ is zero, then line always passes through a fixed point $\left(\bar{x},\bar{y}\right)$ where $\bar{x}=\frac{\sum x_i}{n}$ and $\bar{y}=\frac{\sum y_i}{n}$.
Only S-I is true
Only S-II is true
Both S-I and S-II are True
Both S-I and S-II are false
Step-by-Step Solution
Key Concept: $ax+by+c=0$ is only a line if $a,b$ not both zero; S-II is standard centroid result
S-I: False (if $a=b=0$, $c\ne 0$: no solution; if $a=b=c=0$: all points). S-II: True. Only S-II.
Correct Answer: 2