Open App

Class 10 Exam > Class 10 Notes > Mathematics (Maths) Class 10 > RD Sharma Solutions: Coordinate Geometry (Exercise 7D)

Coordinate Geometry (Exercise 7D) RD Sharma Solutions | Mathematics (Maths) Class 10 PDF Download

Download, print and study this document offline

Please wait while the PDF view is loading

 Page 1


1. Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Sol:
The given points are 1, , 8 5,7 A y and 2, 3 . O y
Here, AO and BO are the radii of the circle. So
2 2
AO BO AO BO
2 2 2 2
2 2 2
2 2
2
2
2
2 1 3 2 5 3 7
9 4 3 3 7
9 16 9 9 49 42
7 42 49 0
6 7 0
7 7 0
7 1 7 0
7 1 0
1 7
y y y
y y
y y y
y y
y y
y y y
y y y
y y
y or y
Hence, 7 1. y or y
2. If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
Sol:
The given ports are 0,2 , 3, A B p and ,5 . C p
Page 2


1. Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Sol:
The given points are 1, , 8 5,7 A y and 2, 3 . O y
Here, AO and BO are the radii of the circle. So
2 2
AO BO AO BO
2 2 2 2
2 2 2
2 2
2
2
2
2 1 3 2 5 3 7
9 4 3 3 7
9 16 9 9 49 42
7 42 49 0
6 7 0
7 7 0
7 1 7 0
7 1 0
1 7
y y y
y y
y y y
y y
y y
y y y
y y y
y y
y or y
Hence, 7 1. y or y
2. If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
Sol:
The given ports are 0,2 , 3, A B p and ,5 . C p
 
2 2
2 2 2 2
2 2
3 0 2 0 5 2
9 4 4 9
4 4 1
AB AC AB AC
p p
p p p
p p
Hence, 1. p
3. ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of
one its diagonal.
Sol:
The given vertices are B(4, 0), C(4, 3) and D(0, 3) Here, BD one of the diagonals So
2 2
2 2
4 0 0 3
4 3
16 9
BD
25
5
Hence, the length of the diagonal is 5 units.
4. If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
Sol:
The given points are 1 ,2 , 3, ,5 . P k A k and B k
2 2
AP BP
AP BP
2 2 2 2
2 2 2 2
2 2
2
1 3 2 1 2 5
4 2 1 3
8 16 4 4 1 9
6 5 0
1 5 0
1 5
k k k k
k k
k y k k
k y
k k
k or k
Hence, 1 5 k or k
5. Find the ratio in which the point P(x,2) divides the join of A(12, 5) and B(4, -3).
Sol:
Let k be the ratio in which the point ,2 P x divides the line joining the points
1 1 2 2
12, 5 4, 3 . A x y and B x y Then
Page 3


1. Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Sol:
The given points are 1, , 8 5,7 A y and 2, 3 . O y
Here, AO and BO are the radii of the circle. So
2 2
AO BO AO BO
2 2 2 2
2 2 2
2 2
2
2
2
2 1 3 2 5 3 7
9 4 3 3 7
9 16 9 9 49 42
7 42 49 0
6 7 0
7 7 0
7 1 7 0
7 1 0
1 7
y y y
y y
y y y
y y
y y
y y y
y y y
y y
y or y
Hence, 7 1. y or y
2. If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
Sol:
The given ports are 0,2 , 3, A B p and ,5 . C p
 
2 2
2 2 2 2
2 2
3 0 2 0 5 2
9 4 4 9
4 4 1
AB AC AB AC
p p
p p p
p p
Hence, 1. p
3. ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of
one its diagonal.
Sol:
The given vertices are B(4, 0), C(4, 3) and D(0, 3) Here, BD one of the diagonals So
2 2
2 2
4 0 0 3
4 3
16 9
BD
25
5
Hence, the length of the diagonal is 5 units.
4. If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
Sol:
The given points are 1 ,2 , 3, ,5 . P k A k and B k
2 2
AP BP
AP BP
2 2 2 2
2 2 2 2
2 2
2
1 3 2 1 2 5
4 2 1 3
8 16 4 4 1 9
6 5 0
1 5 0
1 5
k k k k
k k
k y k k
k y
k k
k or k
Hence, 1 5 k or k
5. Find the ratio in which the point P(x,2) divides the join of A(12, 5) and B(4, -3).
Sol:
Let k be the ratio in which the point ,2 P x divides the line joining the points
1 1 2 2
12, 5 4, 3 . A x y and B x y Then
 
3 5
4 12
2
1 1
k
k
x and
k k
Now,
3 5
3
2 2 2 3 5
1 5
k
k k k
k
Hence, the required ratio is 3: 5.
6. Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and
D(2,6) are equal and bisect each other.
Sol:
The vertices of the rectangle ABCD are 2, 1 , 5, 1 5,6 , A B C and 2,6 . D Now
Coordinates of midpoint of
2 5 1 6 7 5
, ,
2 2 2 2
AC
Coordinates of midpoint of 
5 2 1 6 7 5
, ,
2 2 2 2
BD
Since, the midpoints of AC and BD coincide, therefore the diagonals of rectangle ABCD
bisect each other
7. Find the lengths of the medians AD and BE of ABC whose vertices are A(7,-3), B(5,3)
and C(3,-1)
Sol:
The given vertices are 7, 3 , 5,3 3, 1 . - A B and C
Since D and E are the midpoints of BC and AC respectively. therefore
Coordinates of 
5 3 3 1
, 4,1
2 2
D
Coordinates of 
7 3 3 1
, 5, 2
2 2
E
Now 
2 2
2 2
7 4 3 1 9 16 5
5 5 3 2 0 25 5
AD
BE
Hence, AD = BE = 5 units.
8. If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value
of k.
Sol:
Here, the point ,4 C k divides the join of 2,6 A and 5,1 B in ratio 2 : 3. So
Page 4


1. Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Sol:
The given points are 1, , 8 5,7 A y and 2, 3 . O y
Here, AO and BO are the radii of the circle. So
2 2
AO BO AO BO
2 2 2 2
2 2 2
2 2
2
2
2
2 1 3 2 5 3 7
9 4 3 3 7
9 16 9 9 49 42
7 42 49 0
6 7 0
7 7 0
7 1 7 0
7 1 0
1 7
y y y
y y
y y y
y y
y y
y y y
y y y
y y
y or y
Hence, 7 1. y or y
2. If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
Sol:
The given ports are 0,2 , 3, A B p and ,5 . C p
 
2 2
2 2 2 2
2 2
3 0 2 0 5 2
9 4 4 9
4 4 1
AB AC AB AC
p p
p p p
p p
Hence, 1. p
3. ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of
one its diagonal.
Sol:
The given vertices are B(4, 0), C(4, 3) and D(0, 3) Here, BD one of the diagonals So
2 2
2 2
4 0 0 3
4 3
16 9
BD
25
5
Hence, the length of the diagonal is 5 units.
4. If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
Sol:
The given points are 1 ,2 , 3, ,5 . P k A k and B k
2 2
AP BP
AP BP
2 2 2 2
2 2 2 2
2 2
2
1 3 2 1 2 5
4 2 1 3
8 16 4 4 1 9
6 5 0
1 5 0
1 5
k k k k
k k
k y k k
k y
k k
k or k
Hence, 1 5 k or k
5. Find the ratio in which the point P(x,2) divides the join of A(12, 5) and B(4, -3).
Sol:
Let k be the ratio in which the point ,2 P x divides the line joining the points
1 1 2 2
12, 5 4, 3 . A x y and B x y Then
 
3 5
4 12
2
1 1
k
k
x and
k k
Now,
3 5
3
2 2 2 3 5
1 5
k
k k k
k
Hence, the required ratio is 3: 5.
6. Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and
D(2,6) are equal and bisect each other.
Sol:
The vertices of the rectangle ABCD are 2, 1 , 5, 1 5,6 , A B C and 2,6 . D Now
Coordinates of midpoint of
2 5 1 6 7 5
, ,
2 2 2 2
AC
Coordinates of midpoint of 
5 2 1 6 7 5
, ,
2 2 2 2
BD
Since, the midpoints of AC and BD coincide, therefore the diagonals of rectangle ABCD
bisect each other
7. Find the lengths of the medians AD and BE of ABC whose vertices are A(7,-3), B(5,3)
and C(3,-1)
Sol:
The given vertices are 7, 3 , 5,3 3, 1 . - A B and C
Since D and E are the midpoints of BC and AC respectively. therefore
Coordinates of 
5 3 3 1
, 4,1
2 2
D
Coordinates of 
7 3 3 1
, 5, 2
2 2
E
Now 
2 2
2 2
7 4 3 1 9 16 5
5 5 3 2 0 25 5
AD
BE
Hence, AD = BE = 5 units.
8. If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value
of k.
Sol:
Here, the point ,4 C k divides the join of 2,6 A and 5,1 B in ratio 2 : 3. So
 
2 5 3 2
2 3
10 6
5
16
5
k
Hence, 
16
.
5
k
9. Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
Sol:
Let ,0 P x be the point on . x axis Then
2 2
2 2 2 2
2 2
1 0 0 5 0 0
2 1 10 25
12 24 2
AP BP AP BP
x x
x x x x
x x
Hence, 2 x
10. Find the distance between the points
8
,2
5
A and 
2
,2
5
B
Sol:
The given points are
8
,2
5
A and 
2
,2
5
B
Then, 
1 1 2 2
8 2
, 2 , 2
5 5
x y and x y
Therefore,
2 2
2 1 2 1
2
2
2 2
2 8
2 2
5 5
2 0
4 0
4
2 .
AB x x y y
units
Page 5


1. Points A(-1, y) and B(5,7) lie on the circle with centre O(2, -3y).Find the value of y.
Sol:
The given points are 1, , 8 5,7 A y and 2, 3 . O y
Here, AO and BO are the radii of the circle. So
2 2
AO BO AO BO
2 2 2 2
2 2 2
2 2
2
2
2
2 1 3 2 5 3 7
9 4 3 3 7
9 16 9 9 49 42
7 42 49 0
6 7 0
7 7 0
7 1 7 0
7 1 0
1 7
y y y
y y
y y y
y y
y y
y y y
y y y
y y
y or y
Hence, 7 1. y or y
2. If the point A(0,2) is equidistant from the points B(3,p) and C(p, 5), find p.
Sol:
The given ports are 0,2 , 3, A B p and ,5 . C p
 
2 2
2 2 2 2
2 2
3 0 2 0 5 2
9 4 4 9
4 4 1
AB AC AB AC
p p
p p p
p p
Hence, 1. p
3. ABCD is a rectangle whose three vertices are A(4,0), C(4,3) and D(0,3). Find the length of
one its diagonal.
Sol:
The given vertices are B(4, 0), C(4, 3) and D(0, 3) Here, BD one of the diagonals So
2 2
2 2
4 0 0 3
4 3
16 9
BD
25
5
Hence, the length of the diagonal is 5 units.
4. If the point P(k-1, 2) is equidistant from the points A(3,k) and B(k,5), find the value of k.
Sol:
The given points are 1 ,2 , 3, ,5 . P k A k and B k
2 2
AP BP
AP BP
2 2 2 2
2 2 2 2
2 2
2
1 3 2 1 2 5
4 2 1 3
8 16 4 4 1 9
6 5 0
1 5 0
1 5
k k k k
k k
k y k k
k y
k k
k or k
Hence, 1 5 k or k
5. Find the ratio in which the point P(x,2) divides the join of A(12, 5) and B(4, -3).
Sol:
Let k be the ratio in which the point ,2 P x divides the line joining the points
1 1 2 2
12, 5 4, 3 . A x y and B x y Then
 
3 5
4 12
2
1 1
k
k
x and
k k
Now,
3 5
3
2 2 2 3 5
1 5
k
k k k
k
Hence, the required ratio is 3: 5.
6. Prove that the diagonals of a rectangle ABCD with vertices A(2,-1), B(5,-1) C(5,6) and
D(2,6) are equal and bisect each other.
Sol:
The vertices of the rectangle ABCD are 2, 1 , 5, 1 5,6 , A B C and 2,6 . D Now
Coordinates of midpoint of
2 5 1 6 7 5
, ,
2 2 2 2
AC
Coordinates of midpoint of 
5 2 1 6 7 5
, ,
2 2 2 2
BD
Since, the midpoints of AC and BD coincide, therefore the diagonals of rectangle ABCD
bisect each other
7. Find the lengths of the medians AD and BE of ABC whose vertices are A(7,-3), B(5,3)
and C(3,-1)
Sol:
The given vertices are 7, 3 , 5,3 3, 1 . - A B and C
Since D and E are the midpoints of BC and AC respectively. therefore
Coordinates of 
5 3 3 1
, 4,1
2 2
D
Coordinates of 
7 3 3 1
, 5, 2
2 2
E
Now 
2 2
2 2
7 4 3 1 9 16 5
5 5 3 2 0 25 5
AD
BE
Hence, AD = BE = 5 units.
8. If the point C(k,4) divides the join of A(2,6) and B(5,1) in the ratio 2:3 then find the value
of k.
Sol:
Here, the point ,4 C k divides the join of 2,6 A and 5,1 B in ratio 2 : 3. So
 
2 5 3 2
2 3
10 6
5
16
5
k
Hence, 
16
.
5
k
9. Find the point on x-axis which is equidistant from points A(-1,0) and B(5,0)
Sol:
Let ,0 P x be the point on . x axis Then
2 2
2 2 2 2
2 2
1 0 0 5 0 0
2 1 10 25
12 24 2
AP BP AP BP
x x
x x x x
x x
Hence, 2 x
10. Find the distance between the points
8
,2
5
A and 
2
,2
5
B
Sol:
The given points are
8
,2
5
A and 
2
,2
5
B
Then, 
1 1 2 2
8 2
, 2 , 2
5 5
x y and x y
Therefore,
2 2
2 1 2 1
2
2
2 2
2 8
2 2
5 5
2 0
4 0
4
2 .
AB x x y y
units
 
11. Find the value of a, so that the point 3,a lies on the line represented by 2 3 5. x y
Sol:
The points 3,a lies on the line 2 3 5. x y
If point 3,a lies on the line 2 3 5, x y then 2 3 5 x y
2 3 3 5
6 3 5
3 1
1
3
a
a
a
a
Hence, the value of a is
1
.
3
12. If the points 4,3 ,5 A and B x lie on the circle with center 2,3 , O find the value of x.
Sol:
The given points A(4, 3) and B(x, 5) lie on the circle with center O(2, 3).
Then, OA = OB
2 2 2 2
2 5 3 4 2 3 3 x
2
2 2 2
2
2 2
2 2 2 0
2 2 2
x
x
2
2 0
2 0
2
x
x
x
Hence, the value of 2 x
13. If , P x y is equidistant from the points 7,1 3,5 , A and B find the relation between x
and y.
Sol:
Let the point P(x, y) be equidistant from the points A(7, 1) and B(3, 5)
Then,
2 2
2 2 2 2
7 1 3 5
PA PB
PA PB
x y x y
2 2 2 2
14 2 50 6 10 34 x y x y x y x y
8 8 16 x y
2 x y

	Mathematics (Maths) Class 10 124 videos\|457 docs\|77 tests

Mathematics (Maths) Class 10

124 videos|457 docs|77 tests

Join Course for Free

Top Courses for Class 10

View all

Related Exams

Class 10

About this Document

	4.73/5 Rating
	Nov 08, 2024 Last updated

Document Description: RD Sharma Solutions: Coordinate Geometry (Exercise 7D) for Class 10 2024 is part of Mathematics (Maths) Class 10 preparation. The notes and questions for RD Sharma Solutions: Coordinate Geometry (Exercise 7D) have been prepared according to the Class 10 exam syllabus. Information about RD Sharma Solutions: Coordinate Geometry (Exercise 7D) covers topics like and RD Sharma Solutions: Coordinate Geometry (Exercise 7D) Example, for Class 10 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RD Sharma Solutions: Coordinate Geometry (Exercise 7D).

Introduction of RD Sharma Solutions: Coordinate Geometry (Exercise 7D) in English is available as part of our Mathematics (Maths) Class 10 for Class 10 & RD Sharma Solutions: Coordinate Geometry (Exercise 7D) in Hindi for Mathematics (Maths) Class 10 course. Download more important topics related with notes, lectures and mock test series for Class 10 Exam by signing up for free. Class 10: Coordinate Geometry (Exercise 7D) RD Sharma Solutions | Mathematics (Maths) Class 10

Description

Full syllabus notes, lecture & questions for Coordinate Geometry (Exercise 7D) RD Sharma Solutions | Mathematics (Maths) Class 10 - Class 10 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 10 | Best notes, free PDF download

Information about RD Sharma Solutions: Coordinate Geometry (Exercise 7D)

In this doc you can find the meaning of RD Sharma Solutions: Coordinate Geometry (Exercise 7D) defined & explained in the simplest way possible. Besides explaining types of RD Sharma Solutions: Coordinate Geometry (Exercise 7D) theory, EduRev gives you an ample number of questions to practice RD Sharma Solutions: Coordinate Geometry (Exercise 7D) tests, examples and also practice Class 10 tests

	Mathematics (Maths) Class 10 124 videos\|457 docs\|77 tests

Mathematics (Maths) Class 10

124 videos|457 docs|77 tests

Join Course for Free

Download as PDF

Explore Courses for Class 10 exam

Top Courses for Class 10

Explore Courses

Signup for Free!

Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.

Start learning for Free

10M+ students study on EduRev

video lectures

practice quizzes

Summary

Free

past year papers

Viva Questions

MCQs

mock tests for examination

shortcuts and tricks

Coordinate Geometry (Exercise 7D) RD Sharma Solutions | Mathematics (Maths) Class 10

Important questions

Sample Paper

Exam

Coordinate Geometry (Exercise 7D) RD Sharma Solutions | Mathematics (Maths) Class 10

Objective type Questions

Extra Questions

ppt

Previous Year Questions with Solutions

pdf

study material

Semester Notes

Coordinate Geometry (Exercise 7D) RD Sharma Solutions | Mathematics (Maths) Class 10

;

Additional Information about RD Sharma Solutions: Coordinate Geometry (Exercise 7D) for Class 10 Preparation

RD Sharma Solutions: Coordinate Geometry (Exercise 7D) Free PDF Download

The RD Sharma Solutions: Coordinate Geometry (Exercise 7D) is an invaluable resource that delves deep into the core of the Class 10 exam. These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective. With the help of these notes, you can grasp complex subjects quickly, revise important points easily, and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner, allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material, or toppers' notes, this PDF has got you covered. Download the RD Sharma Solutions: Coordinate Geometry (Exercise 7D) now and kickstart your journey towards success in the Class 10 exam.

Importance of RD Sharma Solutions: Coordinate Geometry (Exercise 7D)

The importance of RD Sharma Solutions: Coordinate Geometry (Exercise 7D) cannot be overstated, especially for Class 10 aspirants. This document holds the key to success in the Class 10 exam. It offers a detailed understanding of the concept, providing invaluable insights into the topic. By knowing the concepts well in advance, students can plan their preparation effectively. Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.

RD Sharma Solutions: Coordinate Geometry (Exercise 7D) Notes

RD Sharma Solutions: Coordinate Geometry (Exercise 7D) Notes offer in-depth insights into the specific topic to help you master it with ease. This comprehensive document covers all aspects related to RD Sharma Solutions: Coordinate Geometry (Exercise 7D). It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation. Practice papers and question papers enable you to assess your progress effectively. Additionally, the paper analysis provides valuable tips for tackling the exam strategically. Access to Toppers' notes gives you an edge in understanding complex concepts. Whether you're a beginner or aiming for advanced proficiency, RD Sharma Solutions: Coordinate Geometry (Exercise 7D) Notes on EduRev are your ultimate resource for success.

RD Sharma Solutions: Coordinate Geometry (Exercise 7D) Class 10 Questions

The "RD Sharma Solutions: Coordinate Geometry (Exercise 7D) Class 10 Questions" guide is a valuable resource for all aspiring students preparing for the Class 10 exam. It focuses on providing a wide range of practice questions to help students gauge their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation. The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level. Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.

Study RD Sharma Solutions: Coordinate Geometry (Exercise 7D) on the App

Students of Class 10 can study RD Sharma Solutions: Coordinate Geometry (Exercise 7D) alongwith tests & analysis from the EduRev app, which will help them while preparing for their exam. Apart from the RD Sharma Solutions: Coordinate Geometry (Exercise 7D), students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc. The EduRev App will make your learning easier as you can access it from anywhere you want. The content of RD Sharma Solutions: Coordinate Geometry (Exercise 7D) is prepared as per the latest Class 10 syllabus.

Education Revolution