Straight Lines ...

The area of the triangle with vertices at $$(-4, 1), (1, 2)(4, -3)$$ is

Given the family of lines $$a(2x+y+4)+b(x-2y-3)=0$$. The numbers of lines belonging to the family at a distance $$\sqrt { 10 } $$ from any point $$(2,-3)$$ is

The coordinates of the point where the line joining $$P(3, 4, 1)$$ and $$Q(5, 1, 6)$$ crosses the xy-plane are:

The area of the triangle whose vertices are (3,8), (-4,2) and (5,-1) is 

For points $$A(1, -1, 1), B(1, 3, 1), C(4, 3, 1)$$ and $$D(4, -1, 1)$$ taken in order are the vertices of

The sides $$AB,BC,CD$$ and $$DA$$ of quadrilateral are $$x+2y=3,x-3y=4,\ 5x+y+12=0$$ respectively. The angle between diagonals $$AC$$ and $$BD$$ is 

If the distance between the points$$\left( {x,2} \right)$$and$$\left( {3,4} \right)$$ is $$2$$,then the value of $$x$$ is

If the axes are transformed from origin to the point $$(-2,1)$$, then new coordinates of $$(4,-5)$$ are

If $$a, b, c$$ and $$d$$ are points on a number line such that $$a < b < c < d, b$$ is twice as far from $$c$$ as from $$a,$$ and $$c$$ is twice as far from $$b$$ as from $$d,$$ then what is the value of $$\dfrac{c-a}{d-b}$$ ?

The curve $$y=ax^3+bx^2+cx+5$$ touches the x-axis at $$P(-2,0)$$ and cuts the y-axis at a point $$Q$$ where its gradient is $$3$$. Then the value of $${a,b,c} $$ is