(A) The perpendicular distance $d$ of a line $Ax + By + C = 0$ from a point $(x_1, y_1)$ is given by the formula $d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A

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

(A) The perpendicular distance $d$ of a line $Ax + By + C = 0$ from a point $(x_1, y_1)$ is given by the formula $d = \frac{|Ax_1 + By_1 + C|}{\sqrt{A^2 + B^2}}$.Given the line $12x + 5y - 7 = 0$ and the origin $(0, 0)$,we have $A = 12$,$B = 5$,$C = -7$,$x_1 = 0$,and $y_1 = 0$.Substituting these values into the formula:$d = \frac{|12(0) + 5(0) - 7|}{\sqrt{12^2 + 5^2}}$$d = \frac{|-7|}{\sqrt{144 + 25}}$$d = \frac{7}{\sqrt{169}}$$d = \frac{7}{13}$.

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

Easy

The perpendicular distance of the straight line $12x + 5y = 7$ from the origin is equal to

A
$\frac{7}{13}$
B
$\frac{12}{13}$
C
$\frac{5}{13}$
D
$\frac{1}{13}$

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

Find the set of all values of $a$ such that both the points $(1, 2)$ and $(3, 4)$ lie on the same side of the line $3x - 5y + a = 0$.

EasyAP EAMCET 2017

View Solution

Find the two points on the line $x + y = 4$ which are at a unit distance from the line $4x + 3y = 10$.

Difficult

View Solution

If the points $(1, 2)$ and $(3, 4)$ lie on the same side of the straight line $3x - 5y + a = 0$,then $a$ lies in the set

DifficultAP EAMCET 2013

View Solution

The line $L$ given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

MediumMHT CET 2024

View Solution

$A$ straight line passes through the points $(5,0)$ and $(0,3)$. The length of the perpendicular from the point $(4,4)$ to the line is:

EasyKCET 2014

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

The perpendicular distance of the straight line $12x + 5y = 7$ from the origin is equal to

Similar Questions

Find the set of all values of $a$ such that both the points $(1, 2)$ and $(3, 4)$ lie on the same side of the line $3x - 5y + a = 0$.

Find the two points on the line $x + y = 4$ which are at a unit distance from the line $4x + 3y = 10$.

If the points $(1, 2)$ and $(3, 4)$ lie on the same side of the straight line $3x - 5y + a = 0$,then $a$ lies in the set

The line $L$ given by $\frac{x}{5}+\frac{y}{b}=1$ passes through the point $(13,32)$. The line $K$ is parallel to $L$ and has the equation $\frac{x}{c}+\frac{y}{3}=1$. Then the distance between $L$ and $K$ is

$A$ straight line passes through the points $(5,0)$ and $(0,3)$. The length of the perpendicular from the point $(4,4)$ to the line is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module