Straight LineHardBloom L3
Question
All the points lying inside the triangle formed by the points $(1,3),(5,6)$, and $( - 1,2)$ satisfy:
Options
A.$3x + 2y \geq 0$
B.$2x + y + 1 \geq 0$
C.$- 2x + 11 \geq 0$
D.$2x + 3y - 12 \geq 0$
Solution
Sol. [Key Concept: A point is interior iff it has the same sign as the centroid in each edge expression.]
✔ (a) $3x + 2y \geq \ 0$ holds for all interior points.
✔ (b) $2x + y + 1 \geq \ 0$ holds throughout the triangle.
✔ (c) $- 2x + 11 \geq \ 0$ holds throughout the triangle.
✘ (d) $2x + 3y - 12 \geq \ 0$ fails for interior points (wrong sign).
Create a free account to view solution
View Solution FreeMore Straight Line Questions
The angle between the pair of lines x2 + 2xy − y2 = 0 is -...The image of the pair of lines represented by $ax^{2} + 2hxy + by^{2} = 0$ by the line mirror $y = 0$ is:...The lines x + (a − 1) y + 1 = 0 and 2x + a2y − 1 = 0 are perpendicular if...Let L1 be a straight line passin through the origin and L2 be the straight line x + y = 1. If the ntercepts made by the ...The complex equation of image of the circle |z - 3 - 4i| = 3 about the straight line (1 + i)z + (i - 1) = 0 is -...