Shown below is a right triangle P Q R . Find the value of cos P .Show your work.

Given: P Q R is a right triangle. From the figure P ( - 5 , - 2 ) , R ( 3 , 4 ) Q is 2 units from the x -axis and it is lies in fourth quadrant So, the y -coordinate of Q is - 2 And, Q is 3 units from the y -axis So, the x -axis coordinate of Q is 3 . Thus, the coordinates of Q 3 . - 2 We have P ( - 5 , - 2 ) , Q ( 3 , - 2 ) P Q = 3 + 5 2 + - 2 + 2 2 = 8 2 + 0 2 = 64 + 0 = 64 = 8 units P R = 3 + 5 2 + 4 + 2 2 = 8 2 + 6 2 = 64 + 36 = 100 = 10 units In ∆ P Q R , cos P = P Q P R ⇒ cos P = 8 10 ⇒ cos P = 4 5 Hence, cos P = 4 5

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

Given: The radius of a circle with centre at the origin is 1 2 units. The coordinates of the centre of the circle are 0 , 0 The distance between the origin 0 , 0 and the point ( - y , y ) = 1 2 units. ⇒ - y - 0 2 + ( y - 0 ) 2 = 1 2 ⇒ y 2 + y 2 = 1 2 ⇒ 2 y 2 = 1 2 ⇒ 2 y 2 = 1 4 [by squaring on both sides] ⇒ y 2 = 1 8 ⇒ y = 1 8 or - 1 8 Therefore, the required points are 1 8 , - 1 8 and - 1 8 , 1 8

MEDIUM

10th CBSE

IMPORTANT

Earn 100

For a triangle, the coordinates of the orthocentre and the circumcentre are $(- 4, 8) and (\frac{1}{2}, 1)$ respectively.Find the coordinates of the centroid of the triangle if the centroid divides the distance from the orthocentre to the circumcentre in the ratio $2 : 1$ . Show your steps.

Important Questions on Coordinate Geometry

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 27

On a playground, Parth, Qasim and Ragini are standing at the points $P (2, 4), Q (8, 6) and R (8, 9)$ respectively. Sameer is standing exactly halfway between Parth and Qasim on the line joining Parth and Qasim.

What is the shortest distance, in units, between Sameer and Ragini?

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 28

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

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 30

Shown below is a right triangle $P Q R$ .

Question Image

Find the value of $\cos P$ .Show your work.

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 31

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.

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 32

A (5, 1), B (1, 4) and C (8, 5)

are coordinates of the vertices of triangle

∆ A B C

, then

∆ A B C

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 33

∆ A B C

is a triangle such that

A B : B C = 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

HARD

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 34

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

Question Image

What is the perimeter of $A B O C$ $?$

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 35

Shown below is a map of Giri's neighbourhood.

Question Image

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?

For a triangle, the coordinates of the orthocentre and the circumcentre are (-4,8) and 12,1 respectively.Find the coordinates of the centroid of the triangle if the centroid divides the distance from the orthocentre to the circumcentre in the ratio 2:1. Show your steps.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

For a triangle, the coordinates of the orthocentre and the circumcentre are $(- 4, 8) and (\frac{1}{2}, 1)$ respectively.Find the coordinates of the centroid of the triangle if the centroid divides the distance from the orthocentre to the circumcentre in the ratio $2 : 1$ . Show your steps.