Distance Formula

An ant is walking across a chessboard.

Its current position on the board can be represented by the point $A$ on the coordinate axes as:

The coordinates of the point on the line $x=2$ that will be closest to the ant is

India is seventh-largest country and second in population in the world. It is a country of Asia. Delhi is the capital of India. There are a total of $28$ states and $8$ union territories in India at present. Each state has their capitals. Each state of India has an administrative, legislative and judicial capital some state. These functions are conducted in one capital.

Ravi plotted some capitals as points on a graph paper and named them as $A, B, C, .....$ etc. as shown below:

The list of the cities which are marked in the graph are given using the table:

The coordinates of a point which lies on the $x-$axis and equidistant from New Delhi and Hyderabad are

An ant is walking across a chessboard.

Its current position on the board can be represented by the point $A$ on the coordinate axes as:

The coordinates of the point on the line $y=5$ that will be closest to the ant is

An ant is walking across a chessboard.

Its current position on the board can be represented by the point $A$ on the coordinate axes as:

The distance of the ant from the origin is

An ant is walking across a chessboard.

Its current position on the board can be represented by the point $A$ on the coordinate axes as:

The distance of the ant from the $x$-axis is

India is seventh-largest country and second in population in the world. It is a country of Asia. Delhi is the capital of India. There are a total of $28$ states and $8$ union territories in India at present. Each state has their capitals. Each state of India has an administrative, legislative and judicial capital some state. These functions are conducted in one capital.

Ravi plotted some capitals as points on a graph paper and named them as $A, B, C, .....$ etc. as shown below:

The list of the cities which are marked in the graph are given using the table:

From the graph, the ratio of the distance between Ranchi-Patna and Gandhinagar-Mumbai is

The constellation of Pegasus is named after the winged horse in Greek mythology. According to the myth, when Perseus killed the Gorgon Medusa (whose hair was made of snakes), Pegasus was born from her blood.

In the constellation of Pegasus, the horse's body is represented by four stars called "The Great _____".

The stars at the corners of this quadrilateral can be drawn on a Cartesian plane at $A\left(-1, 5\right), B\left(3, 2\right), C\left(0, -2\right), D\left(-4, 1\right)$.

Hence, the name of quadrilateral which will be filled in the blank will be

The constellation of Pegasus is named after the winged horse in Greek mythology. According to the myth, when Perseus killed the Gorgon Medusa (whose hair was made of snakes), Pegasus was born from her blood.

In the constellation of Pegasus, the horse's body is represented by four stars called "The Great _____".

The stars at the corners of this quadrilateral can be drawn on a Cartesian plane at $A\left(-1, 5\right), B\left(3, 2\right), C\left(0, -2\right), D\left(-4, 1\right)$.

What can you say about the diagonals of the quadrilateral?

The constellation of Pegasus is named after the winged horse in Greek mythology. According to the myth, when Perseus killed the Gorgon Medusa (whose hair was made of snakes), Pegasus was born from her blood.

In the constellation of Pegasus, the horse's body is represented by four stars called "The Great _____".

The stars at the corners of this quadrilateral can be drawn on a Cartesian plane at $A\left(-1, 5\right), B\left(3, 2\right), C\left(0, -2\right), D\left(-4, 1\right)$.

Choose the correct property of the sides of the quadrilateral.

The constellation of Pegasus is named after the winged horse in Greek mythology. According to the myth, when Perseus killed the Gorgon Medusa (whose hair was made of snakes), Pegasus was born from her blood.

In the constellation of Pegasus, the horse's body is represented by four stars called "The Great _____".

The stars at the corners of this quadrilateral can be drawn on a Cartesian plane at $A\left(-1, 5\right), B\left(3, 2\right), C\left(0, -2\right), D\left(-4, 1\right)$.

The length of side $AB$ of the quadrilateral is

India is seventh-largest country and second in population in the world. It is a country of Asia. Delhi is the capital of India. There are a total of $28$ states and $8$ union territories in India at present. Each state has their capitals. Each state of India has an administrative, legislative and judicial capital some state. These functions are conducted in one capital.

Ravi plotted some capitals as points on a graph paper and named them as $A, B, C, .....$ etc. as shown below:

The list of the cities which are marked in the graph are given using the table:

If the distance between New Delhi and Lucknow is approx. $420 \mathrm{km}$ (straight line distance), then the ratio of their original distance and the distance between them on the graph is

Show that $(0,1), (1,2), (2,3)$and $(3,4)$ are collinear.

Show that $(0,2), (1,3), (2,4)$and $(3,5)$ are collinear.

Show that $(1,4), (2,5), (3,6)$and $(4,7)$ are collinear.

Show that $(0,4), (1,6), (2,8)$and $(3,10)$ are collinear.

Find $a$ if the following points are the vertices of a right triangle with $\angle A=90°$.

$A\left(2, 3\right), B\left(7, a\right), C\left(4, 7\right)$

Prove that the points $(1,3), (2,5)$ and $\left(3, 5\right)$ are on the same line.

Find the length of medians of a triangle whose vertices are $(1,-1),(0,4)$ and $(-5,3)$.

If $(0,0)$ and $(3,\sqrt{3})$ are two vertices of an equilateral triangle, then find third vertex.

Using a graph paper to answer the given questions.
(Take $2 cm=1$ unit on both axes)
Plot the points $A(-4, 2)$ and $B(2, 4)$.