The vertices of a triangle are $\mathrm{A}(-1,3), \mathrm{B}(-2,2)$ and $\mathrm{C}(3,-1)$. $A$ new triangle is formed by shifting the sides of the triangle by one unit inwards. Then the equation of the side of the new triangle nearest to origin is :
$x-y-(2+\sqrt{2})=0$
$-\mathrm{x}+\mathrm{y}-(2-\sqrt{2})=0$
$x+y-(2-\sqrt{2})=0$
$x+y+(2-\sqrt{2})=0$
The co-ordinates of the orthocentre of the triangle bounded by the lines, $4x - 7y + 10 = 0; x + y=5$ and $7x + 4y = 15$ is :
The medians $AD$ and $BE$ of a triangle with vertices $A\;(0,\;b),\;B\;(0,\;0)$ and $C\;(a,\;0)$ are perpendicular to each other, if
In a right triangle $ABC$, right angled at $A$, on the leg $AC $ as diameter, a semicircle is described. The chord joining $A$ with the point of intersection $D$ of the hypotenuse and the semicircle, then the length $AC$ equals to
The area enclosed within the curve $|x| + |y| = 1$ is
The equation of base $BC$ of an equilateral triangle is $3x + 4y = 1$ and vertex is $(-3,2),$ then the area of triangle is-