NCERT Solutions Class 10 Maths Chapter 7 – Download PDF

Get here NCERT Solutions Class 10 Maths Chapter 7. These NCERT Solutions for Class 10 of Maths subject includes detailed answers of all the questions in Chapter 7 – Coordinate Geometry provided in NCERT Book which is prescribed for class 10 in schools.

Resource: National Council of Educational Research and Training (NCERT) Solutions
Class: 10th Class
Subject: Maths
Chapter: Chapter 7 – Coordinate Geometry

NCERT Solutions Class 10 Maths Chapter 7- Free Download PDF

NCERT Solutions Class 10 Maths Chapter 7 – Coordinate Geometry

NCERT Solutions For Class 10 Maths Chapter 7 Coordinate Geometry are provided here in a detailed and easy way. Apart from referring to NCERT books, students can also prepare for their Class 10 exams with the help of these solutions, which are formulated by our experts. Coordinate Geometry problems provided here are easy to understand for students for gaining the best results in the board examinations.

Solutions provided here consist of solved questions for coordinate geometry which will help the student to understand the concepts thoroughly and score good marks in their Board exams. Exercise-wise PDFs are also available, which  students can download and access in offline mode too.

In this chapter, students are introduced with various important topics on coordinate geometry class 10 formulas and students learn how to calculate the distance between any two points if their coordinates are given, finding the area of a triangle whose three points are given, etc.

Here are the sub-topics which include the important coordinate geometry formulas with examples, extra questions with revision notes & worksheets.

• Introduction to Coordinate Geometry
• Distance Formula
• Section Formula
• Area of the Triangle

Coordinate geometry class 10 questions with NCERT solutions given here are very simple and are extremely easy to understand and any students can clear their doubts instantly.

NCERT Solutions for Class 10 Maths Chapter 7 Coordinate Geometry Exercises

We are presenting the coordinate geometry class 10 extra questions with solutions prepared by our subject experts. Check the exercise-wise coordinate geometry NCERT solutions for grade 10 below:

• NCERT Solutions Class 10 Maths Chapter 7 Coordinate Geometry Exercise 7.1

1. If the point A (x , y) is equidistant from B (4 , 2) and C (-2 , 4). Find the relation between x and y.

|AB| = (x−5)2+(y−1)2−−−−−−−−−−−−−−−√

= x2+16−8x+y2+4−4y−−−−−−−−−−−−−−−−−−−−−√

|AC| = (x+2)2+(y−5)2−−−−−−−−−−−−−−−√

= x2+4+4x+y2+16−8y−−−−−−−−−−−−−−−−−−−−−√

Since, |AB| = |AC|

⇒ x2+y2−8x−4y+20 = x2+y2+4x−8y+20

⇒      8y – 4y = 4x + 8x

⇒      y = 3x

2. Find the perimeter of a triangle with vertices (0, 8), (0, 0) and (6, 0)

Let the vertices of the △ be P(0, 8), Q(0, 0) and R(6, 0)

∴ PQ = (0)2+(−8)2−−−−−−−−−−√=64−−√=8

∴ QR = (6)2+(0)2−−−−−−−−−√=36−−√=6

∴ RP = (−6)2+(8)2−−−−−−−−−−√=100−−−√=10

∴  Perimeter of △ = 8 + 6 + 10 = 24 units

3.Find the coordinates of the perpendicular bisector of the line segment joining the points P (1, 4) and Q (2, 3), cuts the y-axis.

Here, O (0, y), P (1, 4) and Q (2, 3)

AO = BO

⇒ (0−1)2+(y−4)2−−−−−−−−−−−−−−−√ = (0−2)2+(y−3)2−−−−−−−−−−−−−−−√

⇒ 1+y2+16−8y=4+y2+9−6y

⇒   8y – 6y = 17 -13

⇒   2y = 4

y = 2

∴The required point is (0, 2)

4. The points which divides the line segment joining the points (5, 8) and (1, 2) in ratio 1:2 internally lies in which quadrant?

Now C(1+103,2+163)

∴ C(113,6)

Since, C(113,6) lies in IV quadrant.

5. If A (x2,3) is the mid-point of the line segment joining the points B(4,1) and C(8,7). Find the value of x.

∴4+82=a2

⇒ 24 = 2a

⇒ a = 12

 

6. A line intersects the y-axis at point A and B respectively. If (3, 4) is the mid-point of AB. Find the coordinates of A and B.

Here, x+02=3 ⇒x=6

0+y2=4 ⇒x=8

∴ The coordinates of A and B are (0, 8) and (6, 0).

7. Find the fourth vertex S of a parallelogram PQRS whose three vertices are P (-3, 8), Q (5, 4) and R (6, 2).

Here, −3+62=5+x2⇒x=−1

8+22=4+x2⇒x=3

∴The fourth vertices S of a parallelogram PQRS is S(-1, 3)

8. Find the coordinates of the point which is equidistant from the three vertices of the

△POQ.

Point equidistant from the three vertices of  a right angle triangle is the mid-point of hypotenuse.

⇒(4x+02,0+4y2)⇒(2x,2y)

 

9. Find the area of a triangle with vertices (x, y + z), (y, z + x) and (z, x + y).

Area of the required

△=12|x(z+x−x−y)+y(x+y−y−z)+(y+z−z−x)|

= 12|x(z−y)+y(x−z)+z(y−a)|

= 12|0| = 0.

10. Find the area of a triangle with vertices P (2, 0), Q (6, 0) and R (5, 4)

Area of the required △PQR

= 12|2(0–2)+6(4–0)+5(0–0)|

= 12|24−4|=10 Sq. units.

11. If the points O (0, 0), P (3, 4), Q (x, y) are collinear, then write the relation between x and y.

Since, O (0, 0), P (3, 4), Q (x, y) are collinear.

⇒ Area of a triangle formed by these points vanishes

∴ 12|0(4–y)+3(y−0)+x(0−4)|=0

⇒y−2x=0⇒2x=y

 

12. Find the coordinates of the point O dividing the line segment joining the point P (6, 5)

and Q(2, 10) in the ratio 2:1.

x=2(2)+1(6)5=4+65=2

and y=2(10)+1(5)5=20+55=5

∴ O(2, 5)

13. The line joining A(4, 3) and B(-3, 6) meets y-axis at C. At what ratio dose C divides the line segment AB?

Since R lies on the y-axis, let C be (0, y)

Suppose that the required ratio be z:1

∴x=−3z+4z+1⇒0=−3z+4⇒z=43

∴ The required ratio is 4 : 3.

In coordinate geometry chapter of class 10, solutions, questions are based on several concepts like Coordinates of a point, Parallel and Perpendicular Lines, Distance Formula & Section formula, Area of triangle, Locus of a point, Transformation of axis, Concepts of straight line, Conic Section (Parabola & Hyperbola, Circle, Ellipse, Pair of straight lines) and more. These concepts are extremely important for class 10 board exam, covering CBSE syllabus, as almost 6 marks are included in the exam from this chapter.

All these concepts are extremely crucial as questions are asked in the 10th class competitive exams. Students are required to be thorough with all the topics that are included in this chapter 7 and should understand the NCERT solved examples properly.

Students also need to solve exercise problems in this chapter and can refer to this NCERT Solutions for Class 10 Maths Coordinate Geometry in case of any doubts. Apart from this, students can also find the solutions for all the chapters by visiting NCERT Solutions For Class 10 Maths.