2d geometry system practice · Mixed difficulty

The area of a triangle, two of whose vertices are $(2,1)$ and $(3,-2)$ is 5 . The coordinates of the third vertex can not be

The figure formed by four points (1,-2), (3, 6), (5,10) and $(3,2)$ is a

A point $P$ moves so that the sum of squares of its distances from the points $(1,2)$ and $(-2,1)$ is 14 . Let $f(x, y)=0$ be the locus of $P$, which intersects the $x$-axis at the points $A, B$ and the $y$-axis at the points $C, D$. Then the area of the quadrilateral $A C B D$ is equal to

If $A$ is $(2,5), B$ is $(4,-11)$ and $C$ lies on $9 x+7 y+4=0$, then the locus of the centroid of the $\Delta A B C$ is a straight line parallel to the straight line is

A point moves so that its distance from the point $(-1,0)$ is always three times its distance from the point $(0,2)$. The locus of the point is

If the circumcentre of a triangle lies at the origin and the centroid is the middle point of the line joining the points $\left(a^2+1, a^2+1\right)$ and $(2 a,-2 a)$, then the orthocentre satisfies the equation

A straight line passes through a fixed point $(h, k)$. The locus of the foot of perpendicular on it drawn from the origin is

If the coordinates of the points $A, B, C$, be $(4,4),(3,-2)$ and $(3,-16)$ respectively, then the area of the triangle $A B C$ is

The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point $(a, b)$, is

If the point $(a, a)$ fall between the lines $|x+y|=2$, then

The orthocentre of the triangle formed by the lines $x y=0$ and $x+y=1$ is

If the points $A(1,1), B(-1,-1)$ and $C(-\sqrt{3}, \sqrt{3})$ are the vertices of $a$ triangle, then the triangle is

The equation of the locus of all points equidistant from the point $(4,2)$ and the $x$-axis, is

A point moves such that its distance from the point $(4,0)$ is half that of its distance from the line $x=16$. The locus of this point is

The area of a parallelogram formed by the lines $a x \pm b y \pm c=0$, is

The distance of any point $P(x, y)$ from the point $Q\left(x_1, y_1\right)$ is given by $d(P, Q)=M a x\{| x-x_1|,| y-y_1 \mid\}$. If $Q(1,2)$ and $d(P, Q)=3$ then locus of $P$ is

The locus of a point which moves so that it is always equidistant from the point $A(a, 0)$ and $B(-a, 0)$ is

A line meets $x$-axis at $A$ and $y$-axis at $B$ such that incentre of the triangle $O A B$ is $(1,1)$. Equation of $A B$ is

The coordinates of incentre of $\triangle A B C$, where $A(-3,-2), B(5,0)$ and $C\left(-\frac{1}{3}, \frac{13}{3}\right)$ are

Let $A\left(x_1, y_1\right), B\left(x_2, y_2\right)$ and $C\left(x_3, y_3\right)$ be the vertices of a triangle such that algebraic sum of perpendicular distance from $A, B$ and $C$ to the variable line $a x+b y+c=0$ is always '0'. If $3 a+2 b+c=0$, then find the value of $\sum\limits_{{i=1}}^3\left(x_i+y_i\right)$.

If the points $A(3,4), B(7,7), C(a, b)$ be collinear and $A C=10$, then $(a, b)=$

The extremities of a diagonal of a parallelogram are the points $(3,-4)$ and $(-6,5)$. If third vertex is $(-2$, 1) then the coordinates of the fourth vertex are

The orthocentre of the triangle formed by the lines $x y=0$ and $2 x+3 y-5=0$ is

If the points $(1,1)(-1,-1)(-\sqrt{3}, \sqrt{3})$ are the vertices of a triangle, then this triangle is

The centroid of a triangle, whose vertices are $(2,1),(5,2)$ and $(3,4)$, is

If $A(-a, 0)$ and $B(a, 0)$ are two fixed points, then the locus of the point on which the line $A B$ subtends the right angle, is

If vertices of $\Delta$ are $(8,-2),(2,-2)\, \&\,(8,6)$, then find its orthocenter

If $\Delta_1$ is the area of the triangle formed by the centroid and two vertices of a triangle, $\Delta_2$ is the area of the triangle formed by the mid-points of the sides of the same triangle, then $\Delta_1: \Delta_2=$

If a vertex of a triangle is $(1,1)$ and the mid-points of two sides through this vertex are $(-1,2)$ and $(3,2)$, then the centroid of the triangle, is

The area of the quadrilateral whose vertices are $(1,2),(6,2),(5,3)$ and $(3,4)$, is