Class 11MathematicsStraight LineDistance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line
MediumStatement $(A)$: The points $(2, 1)$ and $(-3, 5)$ lie on opposite sides of the line $3x - 2y + 1 = 0$.
Reason $(R)$: The algebraic perpendicular distances from the given points to the line have opposite signs.
Reason $(R)$: The algebraic perpendicular distances from the given points to the line have opposite signs.
- A$A$ and $R$ are both independently true and $R$ is the correct explanation for $A$.
- B$A$ and $R$ are both independently true and $R$ is not the correct explanation for $A$.
- C$A$ is true but $R$ is false.
- D$A$ is false but $R$ is true.
Explore More
Similar Questions
Two points $P(a, 2)$ and $Q(1, b)$ lie on either side of the line $2x - 3y + 1 = 0$. If $P$ is the point of intersection of the lines $4x + 3y + k = 0$ and $3x + 4y + k = 0$,then the range of $b$ is
The positions of the points $(3, 4)$ and $(2, -6)$ with respect to the line $3x - 4y = 8$ are:
Easy
View SolutionThe distance between two parallel lines $3x + 4y - 8 = 0$ and $3x + 4y - 3 = 0$ is given by
Easy
View SolutionIf $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line $x+y+3=0$ such that each of them is at a distance of $\sqrt{5}$ units from the line $x+2y+2=0$,then the value of $|x_1-x_2|$ is:
Let the equation $x(x+2)(12-k)=2$ have equal roots. Then the distance of the point $(k, \frac{k}{2})$ from the line $3x+4y+5=0$ is
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo