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

Let $ABC$ be a triangle with $A(-3, 1)$ and $\angle ACB = \theta$,where $0 < \theta < \frac{\pi}{2}$. If the equation of the median through $B$ is $2x + y - 3 = 0$ and the equation of the angle bisector of $C$ is $7x - 4y - 1 = 0$,then $\tan \theta$ is equal to:

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

The centroid of the triangle formed by the lines $x+y-1=0$,$x-y-1=0$,and $x-3y+3=0$ is

The points $(1,3)$ and $(5,1)$ are opposite vertices of a diagonal of a rectangle. If the other two vertices lie on the line $y=2x+c$,then one of the vertices on the other diagonal is

What type of triangle is formed by the lines $x + y = 0$,$3x + y = 4$,and $x + 3y = 4$?