The triangle formed by the lines $3x + y + 4 = 0$,$3x + 4y - 15 = 0$,and $24x - 7y = 3$ is a/an:

If a diagonal of a square is along the line $8x - 15y = 0$ and one of its vertices is $(1, 2)$,then the equations of the sides of the square passing through this vertex are

The mid-points of the sides of a triangle are $(2, 1)$,$(-1, -3)$,and $(4, 5)$. The coordinates of its vertices are:

Two equal sides of an isosceles triangle are given by $7x-y+3=0$ and $x+y-3=0$. If the slope $m$ of the third side is an integer,then $m=$

If $A(1,3)$ and $C(7,5)$ are two opposite vertices of a square,then find the equation of a side passing through $A$.

Let $ABC$ be a triangle with $\angle B = 90^{\circ}$. Let $AD$ be the bisector of $\angle A$ with $D$ on $BC$. Suppose $AC = 6 \text{ cm}$ and the area of the $\triangle ADC$ is $10 \text{ cm}^2$. Then,the length of $BD$ in $\text{cm}$ is equal to