The radius of a circle with centre at the origin is $\frac{1}{2}$units.
Find all the points on the circle which are of the form $(-y, y)$ . Show your steps.

A quadrilateral $ABOC$  is drawn on a coordinate grid as shown below. $O$ is the origin and the coordinates of $A$ are $(-3,4)$ .$\angle OCA=45°$

What is the perimeter of $ABOC$$?$

Shown below is a map of Giri's neighbourhood.

Giri did a survey of his neighbourhood and collected the following information.
* The hotel, mall and the main gate of the garden lie in a straight line.
* The distance between the hotel and the mall is half the distance between the mall and the main gate of the garden.
* The bus stand is exactly midway between the main gate of the garden and the fire station.
* The mall, bus stand and the water tank lie in a straight line.

How much more is the shortest distance of the school from the water tank than the distance of the school from the police station? 

Shown below is a map of Giri's neighbourhood.

Giri did a survey of his neighbourhood and collected the following information.
* The hotel, mall and the main gate of the garden lie in a straight line.
* The distance between the hotel and the mall is half the distance between the mall and the main gate of the garden.
* The bus stand is exactly midway between the main gate of the garden and the fire station.
* The mall, bus stand and the water tank lie in a straight line.

What is the shortest distance between the water tank and the school? 

Shown below is a map of Giri's neighbourhood.

Giri did a survey of his neighbourhood and collected the following information.
* The hotel, mall and the main gate of the garden lie in a straight line.
* The distance between the hotel and the mall is half the distance between the mall and the main gate of the garden.
* The bus stand is exactly midway between the main gate of the garden and the fire station.
* The mall, bus stand and the water tank lie in a straight line.

What are the coordinates of the fire station? 

Shown below is a map of Giri's neighbourhood.

Giri did a survey of his neighbourhood and collected the following information.
* The hotel, mall and the main gate of the garden lie in a straight line.
* The distance between the hotel and the mall is half the distance between the mall and the main gate of the garden.
* The bus stand is exactly midway between the main gate of the garden and the fire station.
* The mall, bus stand and the water tank lie in a straight line.

What is the $x$-coordinate of the mall's location?

Find the distance between the following pair of points.

$\left(-5,7\right), \left(-1,3\right)$