Embibe Experts Solutions for Exercise 5: Assignment

The sides $AB, BC, CD, DA$ of a quadrilateral have the equations $x+2y=3, x=1, x-3y=4,5x+y=-12$ respectively. Find the angle between the diagonals $AC$ and $BD$.

Find the equations of the medians of the triangle whose vertices are $(2,0),(0,2)$ and $(4,6)$.

The opposite angular points of a square are $(2,0)$ and $(5,1)$. Find the remaining points.

The extremities of the base of an isosceles triangle are the points $(2a, 0)$ and $(0, a)$ and the equation of one of the equal sides is $x=2a$. Find the equation of the other equal side.

One side of a square is inclined to the $x-$axis at an angle $\alpha$ and one of its extremities is at origin. If the side of a square is $4,$ find the equations of the diagonals of the square.

Find the equations of the lines passing through the point $(1,0)$ and at a distance of $\frac{\sqrt{3}}{2}$ units from the origin.

If the line joining two points $A(2,0)$ and $B(3,1)$ is rotated about $A$ in anticlockwise direction through an angle of $15°$, then find the equation of the line in new position.

If one diagonal of a square is along the line $8x-15y=0$ and one of its vertex is at $(1,2)$, then find the equation of sides of the square passing through this vertex.