(B) The lines are $L_1: 2x + y - 3 = 0$ and $L_2: 2x + y - 5 = 0$. These are parallel lines. For $L_1$,the intercepts are $x = 1.5$ $(A)$ and $y = 3$

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Statement-$1$ is false,Statement-$2$ is true

(B) The lines are $L_1: 2x + y - 3 = 0$ and $L_2: 2x + y - 5 = 0$. These are parallel lines. For $L_1$,the intercepts are $x = 1.5$ $(A)$ and $y = 3$ $(B)$. For $L_2$,the intercepts are $x = 2.5$ $(C)$ and $y = 5$ $(D)$. The region between the lines is given by $3 For the point $(2, 3)$,we calculate $2(2) + 3 = 4 + 3 = 7$. Since $7 > 5$,the point $(2, 3)$ does not lie between the lines. Therefore,Statement-$1$ is false. Statement-$2$ is also false because the point does not lie between the lines.

Class 11 Mathematics Straight Line Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

Difficult

Given the lines $y + 2x = 3$ and $y + 2x = 5$ cut the axes at $A, B$ and $C, D$ respectively.
Statement-$1$ : $ABDC$ forms a quadrilateral and the point $(2, 3)$ lies inside the quadrilateral.
Statement-$2$ : The point $(2, 3)$ lies between the two parallel lines.

A
Statement-$1$ is true,Statement-$2$ is true; Statement-$2$ is not the correct explanation of Statement-$1$
B
Statement-$1$ is false,Statement-$2$ is true
C
Statement-$1$ is true,Statement-$2$ is false
D
Statement-$1$ is true,Statement-$2$ is true; Statement-$2$ is the correct explanation of Statement-$1$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Straight Line

Subtopic

Distance between two lines, Perpendicular distance of the line from a point, Position of point w.r.t. line

If $p$ is the length of the perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$,then show that $\frac{1}{p^{2}} = \frac{1}{a^{2}} + \frac{1}{b^{2}}$.

Difficult

View Solution

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

EasyTS EAMCET 2023

View Solution

Let the centroid of an equilateral triangle $ABC$ be at the origin. Let one of the sides of the equilateral triangle be along the straight line $x + y = 3$. If $R$ and $r$ are the radius of the circumcircle and incircle respectively of $\Delta ABC$,then $(R + r)$ is equal to ..... .

MediumJEE MAIN 2021

View Solution

If ${p_1}, {p_2}$ and ${p_3}$ are the perpendicular distances from the points $({m^2}, 2m)$,$(mm', m + m')$ and $(m'^2, 2m')$ respectively to the line $x \cos \alpha + y \sin \alpha + \frac{\sin^2 \alpha}{\cos \alpha} = 0$,then ${p_1}, {p_2}$ and ${p_3}$ are in:

Difficult

View Solution

The equations of the lines passing through the point of intersection of the lines $x - y + 1 = 0$ and $2x - 3y + 5 = 0$ and whose distance from the point $(3, 2)$ is $\frac{7}{5}$ are:

MediumIIT 1963

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

Given the lines $y + 2x = 3$ and $y + 2x = 5$ cut the axes at $A, B$ and $C, D$ respectively. Statement-$1$ : $ABDC$ forms a quadrilateral and the point $(2, 3)$ lies inside the quadrilateral.Statement-$2$ : The point $(2, 3)$ lies between the two parallel lines.

Similar Questions

If $p$ is the length of the perpendicular from the origin to the line whose intercepts on the axes are $a$ and $b$,then show that $\frac{1}{p^{2}} = \frac{1}{a^{2}} + \frac{1}{b^{2}}$.

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

Let the centroid of an equilateral triangle $ABC$ be at the origin. Let one of the sides of the equilateral triangle be along the straight line $x + y = 3$. If $R$ and $r$ are the radius of the circumcircle and incircle respectively of $\Delta ABC$,then $(R + r)$ is equal to ..... .

If ${p_1}, {p_2}$ and ${p_3}$ are the perpendicular distances from the points $({m^2}, 2m)$,$(mm', m + m')$ and $(m'^2, 2m')$ respectively to the line $x \cos \alpha + y \sin \alpha + \frac{\sin^2 \alpha}{\cos \alpha} = 0$,then ${p_1}, {p_2}$ and ${p_3}$ are in:

The equations of the lines passing through the point of intersection of the lines $x - y + 1 = 0$ and $2x - 3y + 5 = 0$ and whose distance from the point $(3, 2)$ is $\frac{7}{5}$ are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Given the lines $y + 2x = 3$ and $y + 2x = 5$ cut the axes at $A, B$ and $C, D$ respectively.
Statement-$1$ : $ABDC$ forms a quadrilateral and the point $(2, 3)$ lies inside the quadrilateral.
Statement-$2$ : The point $(2, 3)$ lies between the two parallel lines.