What type of triangle is formed by the vertices $(-2, 2)$,$(8, -2)$,and $(-4, -3)$?

Let $A \equiv (3, 2)$ and $B \equiv (5, 1)$. An equilateral triangle $ABP$ is constructed on the side of $AB$ remote from the origin. The orthocentre of triangle $ABP$ is:

The equations of the sides $AB$,$BC$ and $CA$ of a triangle $ABC$ are $2x + y = 0$,$x + py = 39$ and $x - y = 3$ respectively and $P(2, 3)$ is its circumcentre. Then which of the following is $NOT$ true?

Suppose $\triangle ABC$ is an isosceles triangle with $\angle C=90^{\circ}$,$A=(2,3)$ and $B=(4,5)$. Then the centroid of the triangle is

Two lines are drawn through $(3, 4)$,each of which makes an angle of $45^\circ$ with the line $x - y = 2$. The area of the triangle formed by these lines is:

Let $A(-2,-1)$,$B(1,0)$,$C(\alpha, \beta)$,and $D(\gamma, \delta)$ be the vertices of a parallelogram $ABCD$. If the point $C$ lies on $2x-y=5$ and the point $D$ lies on $3x-2y=6$,then the value of $|\alpha+\beta+\gamma+\delta|$ is equal to . . . . . . .