If the points $(a, 0)$,$(0, b)$,and $(1, 1)$ are collinear,then:

If the sides $AB, BC, CD$ and $DA$ of a quadrilateral are given by the equations $x + 2y = 3, x = 1, x - 3y = 4$ and $5x + y + 12 = 0$ respectively,then find the angle between the diagonals $AC$ and $BD$ in degrees.

The area of the parallelogram formed by the lines $x \cos \alpha + y \sin \alpha = p$,$x \cos \alpha + y \sin \alpha = q$,$x \cos \beta + y \sin \beta = r$,and $x \cos \beta + y \sin \beta = s$ is:

Suppose $ABCD$ is a trapezium whose sides and height are integers and $AB$ is parallel to $CD$. If the area of $ABCD$ is $12$ and the sides are distinct,then $|AB-CD|$ is:

One of the vertices of a square is the origin,and the adjacent sides of the square lie along the positive $x$ and $y$ axes. If the side length is $5$,which of the following is $NOT$ a vertex of the square?

The equations of the perpendicular bisectors of the sides $AB$ and $AC$ of $\triangle ABC$ are $x-y+5=0$ and $x+2y=0$ respectively. If the coordinates of $A$ are $(1,-2)$,then the equation of the line $BC$ is