The point $(-4, 5)$ is a vertex of a square and one of its diagonals lies along the line $7x - y + 8 = 0$. The equation of the other diagonal is:

For a right-angled triangle having the lengths of two sides as $2 \sqrt{2}$ and $5$,find the possible lengths of the third side.

Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$,respectively. $A$ right-angled triangle $AMN$ is inscribed in the triangle $OAB$,where $O$ is the origin and the points $M$ and $N$ lie on the lines $OB$ and $AB$,respectively. If the area of the triangle $AMN$ is $\frac{4}{9}$ of the area of the triangle $OAB$ and $AN : NB = \lambda : 1$,then the sum of all possible values of $\lambda$ is:

$A$ regular octagon is formed by cutting congruent isosceles right-angled triangles from the corners of a square. If the square has side length $1$,the side length of the octagon is

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

The point $P(3,6)$ is first reflected on the line $y=x$ and then the image point $Q$ is again reflected on the line $y=-x$ to get the image point $Q^{\prime}$. Then, the circumcentre of the $\Delta P Q Q^{\prime}$ is