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

Three vertices of a triangle are $A(4, 3)$,$B(1, -1)$,and $C(7, k)$. The value$(s)$ of $k$ for which the centroid,orthocentre,incentre,and circumcentre of the $\Delta ABC$ lie on the same straight line is/are:

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

Two adjacent sides of a parallelogram are $4x + 5y = 0$ and $7x + 2y = 0$. If the equation of one diagonal is $11x + 7y - 9 = 0$,find the equation of the other diagonal.

Let $P$ be an interior point of a convex quadrilateral $ABCD$ and $K, L, M, N$ be the mid-points of $AB, BC, CD, DA$ respectively. If $\text{Area}(PKAN) = 25$,$\text{Area}(PLBK) = 36$,and $\text{Area}(PMDN) = 41$,then $\text{Area}(PLCM)$ is

If the points $(a, b)$,$(a', b')$ and $(a - a', b - b')$ are collinear,then: