CBSE Class-9 Mathematics (Demo)

If $$\mathrm{A}(-3,2), \mathrm{B}(7,8)$$ and C is a point on X -axis form an Isosceles triangle with vertex at $$C$$, then the length of the median through $$C$$ is,

If the points $$(-2,-1),(1,0),(x, 3)$$ and $$(1, y)$$ in order form a parallelogram, then $$x+y$$ is

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

If $$(3,0),(-1,-6)$$ and $$(4,-1)$$ are any three points on a circle, then the radius of the circle is

If $$(1,2),(5,2)$$ and $$(5,6)$$ are vertices of a triangle, then the distance between its circumcenter and centroid is

The circumcentre of an equilateral triangle is $$(0,0)$$. If $$(-3,-4)$$ is one of the vertices and the second one lies on $$y$$-axis, then the third vertex is

The points $$(-\mathrm{a},-\mathrm{b}),(0,0),(a,b),\left(a^{2}, a b\right)$$ are

If the distance of $$(4,0)$$ from $$(a, b)$$ is double the distance of the point $$(a, b)$$ from the $$x$$-axis, then the relation between $$a$$ and $$b$$ is

If $$(-2,-1)$$ and $$(4,-5)$$ are the opposite vertices of a rectangle, then the correct one among the following is

If two vertices of a triangle are $$(-4,3),(2,6)$$ and the centroid is the origin, then the third vertex is

If the point $$(x, y)$$ be equidistant from the points $$(6,-1)$$ and $$(2,3)$$ ，then＇$$x-y$$＇is equal to

An equilateral triangle has one vertex at the point $$(0,0)$$ and another at $$(3, \sqrt{3})$$ ，then the coordinates of the third vertex are

Let the opposite angular points of a square be（ 3,4 ）and（ $$1,-1$$ ），then the coordinates of the remaining angular points are

The circumcentre of the triangle whose vertices are $$(-2,-3),(-1,0)$$ and $$(7,-6)$$ is

The points $$(a+1,1),(2 a+1,3)$$ and $$(2 a+2,2 a)$$ are collinear if

The number of points on $$x$$－axis which are at a distance $$C$$ units $$(C<3)$$ from $$(2,3)$$ is

The point on the axis of $$y$$ which is equidistant from $$(-1,2)$$ and $$(3,4)$$ is

If $$P\left(a t^{2}, 2 a t\right), Q\left(\frac{a}{t^{2}}, \frac{2 a}{t}\right)$$ and $$S(a, 0)$$ be any three points, then the value of $$\frac{1}{S P}+\frac{1}{S Q}$$ is

The distance between the points $$\left(a t_{1}^{2}, 2 a t_{1}\right)$$ and $$\left(a t_{2}^{2}, 2 a t_{2}\right)$$ ，where $$t_{1}$$ and $$t_{2}$$ are the roots of the equation $$x^{2}-2 \sqrt{3} x+2=0$$ and $$a>0$$ is

If $$a$$ and $$b$$ are real numbers between 0 and 1 such that the points $$(a, 1)$$,  $$(1, b)$$ and $$(0,0)$$ form an equilateral triangle then the values of $$a$$ and $$b$$ are

The line segment joining $$A(6,3)$$ to $$B(-1,-4)$$ is doubled in length by having half of its length added to each end. The co-ordinates of the new ends are

The point whose coordinates are $$x=x_{1}+t\left(x_{2}-x_{1}\right), y=y_{1}+t\left(y_{2}-y_{1}\right)$$ divides the join of $$\left(x_{1}, y_{1}\right)$$ and $$\left(x_{2}, y_{2}\right)$$ in the ratio

If the point $$\left(x_{1}+t\left(x_{2}-x_{1}\right), y_{1}+t\left(y_{2}-y_{1}\right)\right)$$ divides the join of $$\left(x_{1}, y_{1}\right)$$ and $$\left(x_{2}, y_{2}\right)$$ internally, then

$$A(a, b)$$ and $$B(0,0)$$ are two fixed points. $$M_{1}$$ is the midpoint of $$\overline{A B} \cdot M_{2}$$ is the midpoint of $$\overline{A M_{1}}, M_{3}$$ is the midpoint of $$\overline{A M_{2}}$$ and so on, then $$M_{5}$$ is

The length of median through $$A$$ of a triangle whose vertices are $$A(-1,3), B(1,-1)$$ and $$C(5,1)$$ is