2d geometry system practice · Easy

If the point $(x, y)$ is equidistant from the points $(a+b, b-a)$ and $(a-b, a+b)$, then

In $\triangle A B C$, base $B C$ and area of triangle ' $\triangle$ ' are fixed. Locus of the centroid of $\triangle A B C$ is a straight line that is

The centroid of $\Delta A B C$ is $(2,7)$. If $A=(4,8), B=(a, 0)$ and $C=(0, b)$, then

If $(x, 3)$ and $(3,5)$ are the extremities of a diameter of a circle with centre at $(2, y)$, then the values of $x$ and $y$ are

The area of the triangle with vertices at $(a, b+c),(b, c+a)$ and $(c, a+b)$, is

If the vertices of a triangle are $(1,2),(4,-6)$ and $(3,5)$, then its area is

The coordinates of a point on the line $\frac{x-1}{2}=\frac{y+1}{-3}=z$ at a distance $4 \sqrt{14}$ from the point $(1,-1,0)$ nearer the origin are

If the points $(-2,-5),(2,-2),(8, a)$ are collinear, then the value of $a$ is

The coordinates of the points $A$ and $B$ are $(a, 0)$ and $(-a, 0)$ respectively. If a point $P$ moves so that $P A^{2}-P B^{2}=2 k^{2}$, when $k$ is constant, then the equation to the locus of the point $P$, is

If $A(6,3), B(-3,5), C(4,-2)$ and $D(x, 3 x)$ are four points. If the ratio of area of $\triangle D B C$ and $\triangle A B C$ is $1: 2$, then the value of $x$, will be

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

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

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

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

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

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