Properties of Line, Line Segment and Ray

The coordinates of the vertices of an isosceles triangle are shown. The $x$-coordinate of one of the vertices is missing. Which expression represents the missing $x$-coordinate?

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A variable line in a plane passes through a fixed point and meets the coordinate axes at points $A$ and $B$. Then the locus of the mid-point of $AB$ is

Which of the following are the sides of $\angle XYZ$.

In the given figure name any five-line segments. 

Number of points a ray $\overrightarrow{AB}$ has,

The three vertices of a parallelogram taken in order are $(-1,1),(3,1)$ and $(2,2)$ respectively. Find the coordinates of the fourth vertex.

If the middle points of the sides of a triangle are $(1,1),(2,-3)$ and $(3,4)$, find the centroid of the triangle.

The three vertices $A,B,C$ of a parallelogram $ABCD$ are $(–2,–1),(3,0),(1,–2)$ respectively, find the co-ordinates of vertex $D$.

A line has _____ end point.

Given, a triangle with side $AB=8 \mathrm{cm}.$ To get a line segment $A{B}^{\text{'}}=\frac{3}{4}$ of $AB$, at what ratio the line segment $AB$ should be divided?

The number of minimum points required to determine a line.

Let $\alpha , \beta , \gamma , \delta \in Z$ and let $A\left(\alpha , \beta \right), B\left(1, 0\right), C\left(\gamma , \delta \right)$ and $D\left(1, 2\right)$ be the vertices of a parallelogram $ABCD$. If $AB=\sqrt{10}$ and the points $A$ and $C$ lie on the line $3y=2x+1$, then $2\left(\alpha +\beta +\gamma +\delta \right)$ is equal to

If the coordinates of the vertices of the triangle $ABC$ be $\left(-1,\mathrm{ }6\right),\mathrm{ }\left(-3,\mathrm{ }-9\right)$ and $\left(5,\mathrm{ }–8\right)$ respectively, then the equation of the median through $C$ is

Vertices of a quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ are $\mathrm{A}\mathrm{ }\left(1,\mathrm{ }2\right),\mathrm{ }\mathrm{B}\mathrm{ }\left(4,\mathrm{ }6\right),\mathrm{ }\mathrm{C}\mathrm{ }\left(8,\mathrm{ }9\right)$ and $\mathrm{D}\mathrm{ }\left(5,\mathrm{ }5\right)$ . Then quadrilateral $\mathrm{A}\mathrm{B}\mathrm{C}\mathrm{D}$ is

If mid point of $\left(1, a\right)$ and $\left(a+b, 2\right)$ is $\left(-1,\mathrm{ }-1\right)$ then value of $a^2+b^2$ is

The coordinates of midpoints of the sides of a triangle $\mathrm{A}\mathrm{B}\mathrm{C}$ are $\mathrm{D}\left(2,\mathrm{ }1\right),\mathrm{ }\mathrm{E}\left(5,\mathrm{ }3\right),\mathrm{ }\mathrm{F}\left(3,\mathrm{ }7\right)$ . Then sum of lengths of sides of the triangle is

The points $\left(1,\mathrm{ }3\right)$ and $\left(5,\mathrm{ }1\right)$ are the opposite vertices of a rectangle. The other two vertices lie on the line $\mathrm{y}=2\mathrm{x}+\mathrm{c}$ , then the value of $\mathrm{c}$ will be -

If the three vertices of a rectangle taken in order are the points $\mathrm{ }\left(2,\mathrm{ }-2\right),\mathrm{ }\left(8,\mathrm{ }4\right)$ and $\left(5,\mathrm{ }7\right)$ The coordinates of the fourth vertex are:

The mid points of sides of a triangle are $\left(2,\mathrm{ }1\right),\mathrm{ }\left(-1,-3\right)$ and $\left(4,\mathrm{ }5\right)$ . Then the coordinates of its vertices are

If one end of a diameter of the circle ${\mathrm{x}}^2+{\mathrm{y}}^2-\mathrm{ }4\mathrm{x}-\mathrm{ }6\mathrm{y}+11=0$ is $\left(3,\mathrm{ }4\right)$ , then its other end is