If $x_1, x_2, x_3$ and $y_1, y_2, y_3$ are in $G.P.$ with the same common ratio,then the points $(x_1, y_1), (x_2, y_2),$ and $(x_3, y_3)$ are:

The area (in square units) of the triangle formed by the lines $x=0, y=0$ and $3x+4y=12$ is:

For what value of $y$ does the triangle with vertices $A(2, 7)$,$B(4, y)$,and $C(-2, 6)$ form a right angle at $A$?

Let $ABCD$ be a square and let $P$ be a point on segment $CD$ such that $DP:PC=1:2$. Let $Q$ be a point on segment $AP$ such that $\angle BQP=90^{\circ}$. Then,the ratio of the area of quadrilateral $PQBC$ to the area of the square $ABCD$ is

In $\triangle ABC$,the coordinates of the vertex $A$ are $(-3, 1)$. If the equation of the median through $B$ is $2x + y - 3 = 0$ and the equation of the angle bisector of $\angle C$ is $7x - 4y - 1 = 0$,then the equation of the side $BC$ is

The circumcentre of the triangle formed by the lines $x = -2$,$y = -2$ and $x + y + 2 = 0$ is