Straight Lines

Consider the triangle $A B C$ with vertices $A(-2,3), B(2,1)$ and $C$ $(1,2)$. What is the centroid of the tirnalge ABC ?

The area of the figure formed by the lines $a x+b y+c=0$, ax-by $+c=0, a x+b y-c=0$ and $a x-b y-c=0$ is

Consider the lines $y=3 x, y=6 x$ and $y=9$ What is the area of the triangle formed by these lines?

What is the equation of the straight line passing through the point $(2,3)$ and making an intercept on the positive $y$-axis equal to twice its intercept on the positive $x$-axis?

The length of perpendicular from the origin to a line is 5 units and the line makes an angle $120^{\circ}$ with the positive direction of $x$-axis. The equation of the line is

Consider the triangle $A B C$ with vertices $A(-2,3), B(2,1)$ and $C$ $(1,2)$. What is the foot of the altitude from the vertex A of the triangle ABC?

Consider the triangle $A B C$ with vertices $A(-2,3), B(2,1)$ and $C$ $(1,2)$. What is the circumcentre of the triangle ABC ?

The line $3 x+4 y-24=0$ intersects the $x$-axis at $A$ and $y$-axis at $B$. Then the circumcentre of the triangle $O A B$ where $O$ is the origin is

The point of intersection of diagonals of a square $A B C D$ is at the origin and one of its vertices is at $A\{4,2\}$. What is the equation of the diagonal $B D$ ?

Paragraph: ABCD is an isosceles trapezium and AB is parallel to DC . Let $A(2,3), B(4,3), C(5,1)$ be the vertices. Question: What are the coordinates of vertex D ?

The area of a triangle, whose vertices are $(3,4),(5,2)$ and the point of intersection of the lines $x=\mathrm{a}$ and $y=5$, is 3 square units. What is the value of $a$ ?

If a line is perpendicular to the line $5 x-y=0$ and forms a triangle of area 5 square units with co-ordinate axes, then its equation is