NCERT Solutions for Chapter: Coordinate Geometry, Exercise 1: Exercise

A circle with centre $\mathrm{O}(2, -5)$ has a chord with end-points $\mathrm{A}(1, 2)$ and $\mathrm{B}$. $\mathrm{M}(5, -2)$ is the point where the perpendicular to the chord from the centre touches $\mathrm{AB}$.

Find the coordinates of point $\mathrm{B}$. Show your steps with valid reasons.

Preeti and Arun are both driving to their respective offices from the same home. Preeti drives towards the east at an average speed of$30 \mathrm{km}$  per hour for $12$ minutes and then towards the south at an average speed of $60 \mathrm{km}$ per hour for $3$ minutes. Arun drives towards the west at an average speed of $30 \mathrm{km}$ per hour for $4$ minutes and then towards the north at an average speed of $45 \mathrm{km}$ per hour for $4$ minutes.

What is the straight-line distance between Preeti's office and Arun's office? Show your steps and represent the given scenario on the coordinate plane.

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.

$∆ABC$ is a triangle such that $AB:BC=1:2$. Point $A$ lies on the $y$-axis and the coordinates of $B$ and $C$ are known.
Which of the following formula can DEFINITELY be used to find the coordinates of $A$?
i) Section formula
ii) Distance formula

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?