Embibe Experts Solutions for Chapter: Point and Straight Line, Exercise 1: Exercise 1

A variable straight line, drawn through the point of intersection of the straight line $\frac{x}{4}+\frac{y}{2}=1$ and $\frac{x}{2}+\frac{y}{4}=1$ meets the co-ordinate axes in $A$ and $B$. The locus of midpoint of $AB$ is

A variable straight line passes through the points of intersection of the lines $x+2 y=1$ and $2 x-y=1$ and meets the co-ordinate axes in $A$ and $B$. The locus of middle point of $AB$ is

The distance of the point $\left(1,3\right)$ from the line $2x+3y=6$, measured parallel to the line $4x+y=4$, is

What is the angle between the straight lines $\left(m^2-mn\right)y=\left(mn+n^2\right)x+n^3$ and $\left(mn+m^2\right)y=\left(mn-n^2\right)x+m^3,$ where $m>n?$

The equation of perpendicular bisector of the sides $AB$ and $AC$ of a $∆ABC$ are $x-y+5=0$ and $x+2y=0,$ respectively. If the point $A$ is $\left(1,-2\right),$ then the equation of line $BC$ is

Consider the following statements
$1$. The distance between the lines $y=mx+c_1$ and $y=mx+c_2$ is
$\frac{\left|c_1-c_2\right|}{\sqrt{1+m^2}}$

$2$. The distance between the lines $ax+by+c_1=0$
and $ax+by+c_2=0$ is $\frac{\left|c_1-c_2\right|}{\sqrt{a^2+b^2}}.$.
$3$. The distance between the lines $x=c_1$ and $x=c_2$ is $\left|c_1-c_2\right|$

Which of the above statements are correct?

A line passing through $(0,0)$ and perpendicular to $2 x+y+6=0,4 x+2 y-9=0$ then the origin divides the line in the ratio of

A ray of light is sent along the line $x-2 y-3=0$ on reaching the line $3 x-2 y-5=0$ the ray is reflected from it, then the equation of the line containing the reflected ray is