M L Aggarwal Solutions for Chapter: Straight Lines, Exercise 1: EXERCISE

The points $A(0,3),B(-2,a)$ and $C(-1,4)$ are the vertices of a right angled triangle at $A$, find the value of $a$.

For what value of $k$ are the points $(8,1),(k,-4)$ and $(2,-5)$ collinear $?$

Find the coordinates of the centre of the circle inscribed in a triangle whose angular points are $(-36,7),(20,7)$ and $(0,-8)$.

Two points $A$ and $B$ with coordinates $(1,1)$ and $(-2,3)$ respectively are given. Find the locus of a point $P$ such that area of $∆PAB$ is $9$ sq.units.

Are the points $(2,3)$ and $(-1,5)$ on the same side or on opposite sides of the line $y=2x+5 ?$

Show that the points $(3,5)$ and $(-3,-2)$ lie on the same side of the line $3x=7y+8$.

Which of the points $(1,1),(-1,2),(2,3)$ and $(-3,0)$ lie on the same side of the line $4x+3y=5$ on which the origin lies $?$

Prove that the point $P\left(x_1,y_1\right)$ and the origin lie on the same side or on opposite sides of the line $ax+by+c=0$ according as $a{x}_1+b{y}_1+c$ and $c$ have same sign or opposite signs.