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

Three vertices of triangle $ABC$ are $A\left(-1,11\right),B\left(-9,-8\right)$ and $C\left(15,-2\right)$. The equation of angle bisector of angle $A$ is-

Given the four lines with the equations

$x+2y-3=0,3x+4y-7=0$

$2x+3y-4=0,4x+5y-6=0$

then

The co-ordinates of the point of reflection of the origin $\left(0,0\right)$ in the line $4x-2y-5=0$ is

If the axes are rotated through an angle of $30°$ in the anti-clockwise direction, the coordinates of point $\left(4,-2\sqrt{3}\right)$ with respect to new axes are-

If one diagonal of a square is along the line $x=2y$ and one of its vertex is $\left(3,0\right)$, then its sides through this vertex are given by the equations-

The line $\left(p+2q\right)x+\left(p-3q\right)y=p-q$ for different values of $p$ and $q$ passes through a fixed point whose co-ordinates are-

The equation $2x^2+4xy-p{y}^2+4x+qy+1=0$ will represent two mutually perpendicular straight lines, if-

If the straight lines joining the origin and the points of intersections of the curve $5x^2+12xy-6y^2+4x-2y+3=0$ and $x+ky-1=0$ are equally inclined to the co-ordinate axis, then the value of $k$-