Amit M Agarwal Solutions for Chapter: Straight Line and Pair of Straight Lines, Exercise 1: Work Book Exercise 12.1

If  $A(1,1),B\left(\sqrt{3}+1,2\right)$ and $C\left(\sqrt{3},\sqrt{3}+2\right)$ are three vertices of a square, then the diagonal through $B$ is

If each of the points $\left(x_1,4\right)$ and $\left(-2,y_1\right)$ lies on the line joining the points $(2,-1)$ and $(5,-3),$ then the point $P\left(x_1,y_1\right)$ lies on the line

All points lying inside the triangle formed by the points $(1,3),(5,0)$ and $(-1,2)$ satisfy

A square is constructed on the portion of the line $x+y=5,$ which is intercepted between the axes on the side of the line away from origin. The equations to the diagonals of the square are

A ray of light coming from the point $(1,2)$ is reflected at a point $A$ on the $X$-axis and then passes through the point $(5,3)$. The coordinates of the point $A$ are

The larger of the two angles made with $x$-axis of a straight line drawn through $\left(1,2\right),$ so that it intersects $x+y=4$ at a distance $\frac{\sqrt{6}}{3}$ from $\left(1,2\right),$ is

If two vertices of a triangle are $\left(5,-1\right)$ and $\left(-2,3\right)$ and its orthocentre lies at the origin, then the coordinates of the third vertex are

The equations of the line on which the perpendiculars from the origin make ${30}^{°}$ angle with $x$-axis and which form a triangle of area $\frac{50}{\sqrt{3}}$ with axes, are