Given two points $A(3, 4)$ and $B(5, -2)$. If $PA = PB$ and the area of $\Delta PAB = 10$ square units,find the coordinates of point $P$.

Let a triangle be bounded by the lines $L_{1}: 2x + 5y = 10$,$L_{2}: -4x + 3y = 12$,and the line $L_{3}$,which passes through the point $P(2, 3)$,intersects $L_{2}$ at $A$ and $L_{1}$ at $B$. If the point $P$ divides the line segment $AB$ internally in the ratio $1:3$,then the area of the triangle is equal to

The points $\left( \frac{a}{\sqrt{3}}, a \right)$,$\left( \frac{2a}{\sqrt{3}}, 2a \right)$,and $\left( \frac{a}{\sqrt{3}}, 3a \right)$ are the vertices of:

Find the incenter of the triangle formed by the axes and the line $\frac{x}{a} + \frac{y}{b} = 1$.

In the figure given below,a rectangle of perimeter $76$ units is divided into $7$ congruent rectangles. What is the perimeter of each of the smaller rectangles?

Two sides of a triangle have lengths $a \text{ cm}$ and $b \text{ cm}$. If the triangle is to have the maximum area,then the length of the median from the vertex containing the sides $a$ and $b$ is