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

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

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

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.

If the distance of the point $P\left(-5,5\right)$ from the origin is $k\sqrt{2}$ find the value of $k$

Find the distance between the points $P\left(9,-12\right)$ and $Q\left(-6,-4\right)$. 

If the point $(x,y)$ is equidistant from the point $(7,1)$ and point $(3,5)$, then the relation between $x$ and $y$ is $x-y=2$.

The distance between the point $\mathrm{A}(\sin \mathrm{\theta }-\cos \mathrm{\theta }, 0)$ and $\mathrm{B}(0, \sin \mathrm{\theta }+\cos \mathrm{\theta })$ is $\sqrt{2}$.

For what value of $k$, the points $(8,1),(k,-4)$ and $(2,-5)$ are collinear $?$

A point $\mathrm{P}(5, 2)$ is equidistant from the points $(\mathrm{b}, 10)$ and $(0, \mathrm{b})$. Find $\mathrm{b}$.

Find the distance between the origin and the point: $(-15, 8)$

Find the distance between the origin and the point: $(-12, 5)$