P Q is a line segment such that the y -coordinate of P is - 1 and Q lies on y -axis. The mid-point of P Q is O - 3 , - 6 . Find the coordinates of Q

Given: The y -coordinate of P is - 1 and Q lies on y -axis. Let x -coordinate of P be x Thus, we have P x , - 1 As we know, if any point lies on y -axis, then its x -coordinate is zero.So, the coordinates of Q be Q 0 , y The mid-point of P Q is O - 3 , - 6 . The midpoint of P Q is O = x 1 + x 2 2 , y 1 + y 2 2 ⇒ - 3 , - 6 = x + 0 2 , - 1 + y 2 ⇒ - 3 , - 6 = x 2 , - 1 + y 2 By comparing x -coordinates we get: x 2 = - 3 ⇒ x = - 6 By comparing y -coordinate we get: - 1 + y 2 = - 6 ⇒ y = - 12 + 1 ⇒ y = - 11 Therefore, the coordinates of the point Q 0 , - 11

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

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

Find the coordinates of point $B$ . Show your steps with valid reasons.

Important Questions on Coordinate Geometry

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 22

P Q

is a line segment such that the

y

-coordinate of

P

- 1

and

Q

lies on

y

-axis. The mid-point of

P Q

O (- 3, - 6)

. Find the coordinates of

Q

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 25

Raaji and Gagan are finding a treasure that is exactly on the straight line joining them. Raaji's location is at

(- 6, - 5)

and Gagan's location is at

(10, 11)

. The distance from the treasure to Raaji's location is three times that of the distance to Gagan's location.Find the coordinates of the location of the treasure.

MEDIUM

10th CBSE

IMPORTANT

Mathematics Textbook of Competency Based Questions for Class X>Chapter 7 - Coordinate Geometry>Exercise>Q 26

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.

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

A circle with centre O(2, -5) has a chord with end-points A(1, 2) and B. M(5, -2) is the point where the perpendicular to the chord from the centre touches AB. Find the coordinates of point B. Show your steps with valid reasons.

Important Questions on Coordinate Geometry

Learn and Prepare for any exam you want !

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

Find the coordinates of point $B$ . Show your steps with valid reasons.