Amit M Agarwal Solutions for Chapter: Cartesian System of Rectangular Coordinates, Exercise 1: Work Book Exercise

 The diagonals of a parallelogram $PQRS$ are along the lines $x+3y=4$ and $6x-2y=7$. Then, $PQRS$ must be a

The coordinates of three consecutive vertices of a parallelogram are $(1,3),(-1,2)$ and $(2,5).$ The coordinates of the fourth vertex are

In a $\mathrm{\Delta }ABC,$ the coordinates of $B$ are $(0,0),$ $AB=2,\angle ABC=\frac{\pi }{3}$ and the middle point of $BC$ has the coordinates $(2,0)$. The centroid of the triangle is

The points $\left(\alpha ,\beta \right), \left(\alpha ,\delta \right), \left(\gamma ,\delta \right)$ and $\left(\gamma ,\beta \right)$ taken in order, where $\alpha , \beta , \gamma , \delta$ are different real numbers, are

The limiting position of the point of intersection of the lines $3x+4y=1$ and $(1+c)x+3c^{2}y=2$ as $c$ tends to $1$, is

A point moves in the $xy$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $3$. The area enclosed by the locus of the point is

Three vertices of a quadrilateral in order are $(6,1),(7,2)$ and $(-1,0)$ . If the area of the quadrilateral is $4 \mathrm{sq}$ units, then the locus of fourth vertex has the equation

If a vertex of an equilateral triangle is the origin and the side opposite to it has the equation $x+y=1,$ then the orthocentre of triangle is