Mathematics · Textbook solutions

Coordinate Geometry

Every solved example, exercise, and miscellaneous question, in the order the textbook teaches them. Plus every board question asked from this chapter. · 34 questions

7.2 Distance Formula

19 q

Solved Examples

Worked · 5

7.1 Eg.1 $(3, 2)$
7.1 Eg.2 $(1, 7)$
7.1 Eg.3 $(3, 1)$
7.1 Eg.4 $x$
7.1 Eg.5 $y$

Exercise 7.1

Practice · 14

Find the distance between the following pairs of points :
Ex 7.1 Q1 (i) $(2, 3)$
Ex 7.1 Q1 (ii) $(-5, 7)$
Ex 7.1 Q1 (iii) $(a, b)$
Ex 7.1 Q2 $(0, 0)$
Ex 7.1 Q3 $(1, 5)$
Ex 7.1 Q4 $(5, -2)$
Ex 7.1 Q5 $In a classroom, 4 friends are seated at the points A, B, C and D as shown in Fig. 7.8. Champa and Chameli walk into the class and after observing for a few minutes Champa asks Chameli, “Don’t you think ABCD is a square?” Chameli disagrees. Using distance formula, find which of them is correct.$
Ex 7.1 Q7 $x$
Ex 7.1 Q8 $y$
Ex 7.1 Q9 $(0, 1)$
Ex 7.1 Q10 $x$
Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer:
Ex 7.1 Q6 (i) $(-1, -2)$
Ex 7.1 Q6 (ii) $(-3, 5)$
Ex 7.1 Q6 (iii) $(4, 5)$

7.3 Section Formula

15 q

Solved Examples

Worked · 5

7.2 Eg.6 $(4, -3)$
7.2 Eg.7 $(-4, 6)$
7.2 Eg.8 $(2, -2)$
7.2 Eg.9 $y$
7.2 Eg.10 $(6, 1)$

Exercise 7.2

Practice · 10

Ex 7.2 Q1 $(-1, 7)$
Ex 7.2 Q2 $(4, -1)$
Ex 7.2 Q3 $\dfrac{1}{4}$
Ex 7.2 Q4 $(-3, 10)$
Ex 7.2 Q5 $(1, -5)$
Ex 7.2 Q6 $(1, 2)$
Ex 7.2 Q7 $(2, -3)$
Ex 7.2 Q8 $(-2, -2)$
Ex 7.2 Q9 $(-2, 2)$
Ex 7.2 Q10 $(3, 0)$

What the board has asked from this chapter

Questions per paper · 63 papers · 2023 to 2026

2026

30 q

2 $P(-4, -2)$
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Section Formula and Ratio of Division
7 $(1, 2)$
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Distance Formula
8 $(5, -4)$
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Section Formula and Ratio of Division
9 $A(4a, 3a)$
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Distance Formula
9 $(-1, 2)$
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Distance Formula
10 $(4, p)$
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Distance Formula
15 $(a\cos\theta + b\sin\theta, 0)$
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Distance Formula
17 $\Delta ABC$
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Distance Formula
21 $(4, p)$
Distance Formula
21 $\Delta ABC$
Section Formula and Ratio of Division
21 $(1, 0)$
Distance Formula
22 (a) $\angle B = 90^\circ$
Distance Formula
22 (b) $A(2, 3)$
Distance Formula
23 (a) $(9, -2)$
Section Formula and Ratio of Division
23 $(x - 7, 2x)$
Distance Formula
23 $A(4, 5)$
Section Formula and Ratio of Division
23 (b) $x + y = 5$
Distance Formula
27 $A(-1, 4)$
Section Formula and Ratio of Division
27 $x$
Section Formula and Ratio of Division
27 $A(-3, 5)$
Section Formula and Ratio of Division
28 $3x + y - 9 = 0$
Section Formula and Ratio of Division
29 $P(2, -3)$
Section Formula and Ratio of Division
29 (a) $(2, 1)$
Distance Formula
30 $P(x, 7)$
Section Formula and Ratio of Division
29 (b) $A(-1, 7)$
Section Formula and Ratio of Division
31 $(-6, -5)$
Section Formula and Ratio of Division
Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : $(-4, 2)$ Rajasthan High Court Point B : $(4, -4)$ Birla Mandir Point C : $(4, 3)$ Heera Bagh Point D : $(-5, -2)$ Amar Jawan Jyoti Based on the above, answer the following questions :
38 (i) $Advocate Rehana stays at Heera Bagh. How much distance she has to cover daily to go to the court and coming back home ?$
Distance Formula
Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : $(-4, 2)$ Rajasthan High Court Point B : $(4, -4)$ Birla Mandir Point C : $(4, 3)$ Heera Bagh Point D : $(-5, -2)$ Amar Jawan Jyoti Based on the above, answer the following questions :
38 (ii) $There is a crossing on X-axis which divides AD in a certain ratio. Find the ratio.$
Section Formula and Ratio of Division
Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : $(-4, 2)$ Rajasthan High Court Point B : $(4, -4)$ Birla Mandir Point C : $(4, 3)$ Heera Bagh Point D : $(-5, -2)$ Amar Jawan Jyoti Based on the above, answer the following questions :
38 (iii) (a) $Is Birla Mandir equidistant from Heera Bagh and Amar Jawan Jyoti ? Justify your answer.$
Distance Formula
Observe the map of Jaipur city placed on a Cartesian plane. Taking Rambagh Palace as origin, the location of some places are given below : Point A : $(-4, 2)$ Rajasthan High Court Point B : $(4, -4)$ Birla Mandir Point C : $(4, 3)$ Heera Bagh Point D : $(-5, -2)$ Amar Jawan Jyoti Based on the above, answer the following questions :
38 (iii) (b) $Using section formula, show that points A, O and B are not collinear.$
Section Formula and Ratio of Division

2025

32 q

3 $(0, 0)$
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Distance Formula
3 $P(-4, 5)$
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Section Formula and Ratio of Division
3 $(4, 0)$
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Distance Formula
4 $The distance of a point A from x-axis is 3 units. Which of the following cannot be coordinates of the point A ?$
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Distance Formula
5 $A(-3, -4)$
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Distance Formula
5 $(5, -2)$
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Distance Formula
6 $\dfrac{x}{4} + \dfrac{y}{6} = 1$
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Section Formula and Ratio of Division
6 $The distance of which of the following points from origin is less than 5 units ?$
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Distance Formula
6 $In the figure given below, points P, Q, R divides the line segment AB in four equal parts. The point Q divides PB in the ratio$
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Section Formula and Ratio of Division
6 $(-5, 0)$
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Distance Formula
6 $\dfrac{AB}{PB}$
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Section Formula and Ratio of Division
7 $(a, -b)$
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Distance Formula
7 $\Delta PQR$
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Section Formula and Ratio of Division
13 $P(1, -1)$
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Distance Formula
14 $P(3a, 4a)$
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Distance Formula
15 $(a, 4)$
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Section Formula and Ratio of Division
15 $\dfrac{AB}{PB} =$
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Section Formula and Ratio of Division
16 $(2, 4)$
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Distance Formula
16 $A(0, 2)$
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Distance Formula
22 $A(-2, -2)$
Section Formula and Ratio of Division
23 $(-1, 7)$
Section Formula and Ratio of Division
23 $(2a, a - 7)$
Distance Formula
23 $A(7, 1)$
Distance Formula
25 $\Delta ABC$
Section Formula and Ratio of Division
26 (a) $A(3, 4)$
Section Formula and Ratio of Division
26 (b) $A(-2, 2)$
Section Formula and Ratio of Division
27 $(a, b)$
Section Formula and Ratio of Division
28 $P(x, y)$
Distance Formula
28 $(5, -6)$
Section Formula and Ratio of Division
29 $A(6, 1)$
Section Formula and Ratio of Division
29 $P(x, y)$
Distance Formula
28 $A(3, 4)$
Section Formula and Ratio of Division

2024

32 q

1 $(a\cos\theta, -a\sin\theta)$
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Distance Formula
2 $A(4, -5)$
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Section Formula and Ratio of Division
6 $\Delta ABC$
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Distance Formula
11 $(3, -5)$
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Distance Formula
15 $X(-3, 0)$
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Distance Formula
16 $A(-2, 3)$
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Section Formula and Ratio of Division
17 $(2, 0)$
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Section Formula and Ratio of Division
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below :
19 $A(1, 2)$
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Section Formula and Ratio of Division
Questions number 19 and 20 are Assertion and Reason based questions. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (A), (B), (C) and (D) as given below.
19 $(-3, k)$
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Section Formula and Ratio of Division
22 $A(1, 0)$
Distance Formula
23 (a) $x$
Distance Formula
23 $\Delta OAB$
Distance Formula
24 (a) $P(-4, 6)$
Section Formula and Ratio of Division
24 $\Delta ABC$
Section Formula and Ratio of Division
23 (b) $A(-1, y)$
Section Formula and Ratio of Division
24 (b) $(3, 0)$
Distance Formula
25 (a) $(3, -5)$
Section Formula and Ratio of Division
25 (b) $A(3, 0)$
Section Formula and Ratio of Division
26 (A) $\left(\dfrac{8}{5}, y\right)$
Section Formula and Ratio of Division
26 (B) $A(-1, -1)$
Section Formula and Ratio of Division
28 (a) $(2, -3)$
Section Formula and Ratio of Division
28 (b) $\Delta ABC$
Section Formula and Ratio of Division
29 (a) $(5, 3)$
Section Formula and Ratio of Division
29 (b) $P(-2, 5)$
Section Formula and Ratio of Division
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below : Based on the above, answer the following questions :
36 (i) $Find the mid-point of the segment joining F and G.$
Section Formula and Ratio of Division
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below : Based on the above, answer the following questions :
36 (ii) (a) $What is the distance between the points A and C ?$
Distance Formula
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below : Based on the above, answer the following questions :
36 (ii) (b) $Find the coordinates of the point which divides the line segment joining the points A and B in the ratio 1 : 3 internally.$
Section Formula and Ratio of Division
Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below : Based on the above, answer the following questions :
36 (iii) $What are the coordinates of the point D ?$
Distance Formula
A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class 10. They made a chart for it which looks like the given figure. Based on the above, answer the following questions :
37 (i) $\Delta PQR$
Distance Formula
A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class 10. They made a chart for it which looks like the given figure. Based on the above, answer the following questions :
37 (ii) (a) $Find distances PQ and QR.$
Distance Formula
A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class 10. They made a chart for it which looks like the given figure. Based on the above, answer the following questions :
37 (ii) (b) $2 : 1$
Section Formula and Ratio of Division
A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above situation, the gardener took help from the students of class 10. They made a chart for it which looks like the given figure. Based on the above, answer the following questions :
37 (iii) $\Delta PQR$
Distance Formula

2023

32 q

1 $(0, 5)$
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Distance Formula
2 $(-2, 3)$
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Section Formula and Ratio of Division
2 $(-6, 8)$
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Distance Formula
4 $A(3, 6)$
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Section Formula and Ratio of Division
4 $(-1, 7)$
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Distance Formula
5 $B(0, 0)$
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Section Formula and Ratio of Division
7 $(-4, 3)$
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Distance Formula
7 $(2, 4)$
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Distance Formula
7 $P\left(-\dfrac{11}{3}, 5\right)$
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Distance Formula
13 $(0, 2\sqrt{5})$
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Distance Formula
13 $(-6, 8)$
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Distance Formula
15 $(-5, 4)$
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Distance Formula
17 $\dfrac{x}{a} + \dfrac{y}{b} = 1$
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Distance Formula
18 $(-4, 0)$
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Distance Formula
Questions number 19 and 20 are Assertion and Reason based questions carrying 1 mark each. Two statements are given, one labelled as Assertion (A) and the other is labelled as Reason (R). Select the correct answer to these questions from the codes (a), (b), (c) and (d) as given below.
19 $A(4, 3)$
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Distance Formula
In Question 19 and 20, an Assertion (A) statement is followed by a statement of Reason (R). Select the correct option out of the following :
19 $P(0, 2)$
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Distance Formula
21 (a) $A(4, -5)$
Section Formula and Ratio of Division
21 $(5, -6)$
Section Formula and Ratio of Division
22 $y = x$
Section Formula and Ratio of Division
21 (b) $P(x, y)$
Distance Formula
22 $x$
Section Formula and Ratio of Division
23 $(-2, 3)$
Distance Formula
24 $(5, -6)$
Section Formula and Ratio of Division
24 $x$
Distance Formula
26 $A(6, 3)$
Section Formula and Ratio of Division
26 $(2a, a - 7)$
Distance Formula
28 $(-5, 3)$
Distance Formula
28 $Q(0, 1)$
Distance Formula
Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. Based on the above information, answer the following questions :
37 (i) $(-200, 0)$
Distance Formula
Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. Based on the above information, answer the following questions :
37 (ii) (a) $What is the area of square PQRS ?$
Distance Formula
Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. Based on the above information, answer the following questions :
37 (ii) (b) $What is the length of diagonal PR in square PQRS ?$
Distance Formula
Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. Based on the above information, answer the following questions :
37 (iii) $(200, 800)$
Section Formula and Ratio of Division

The 10 board questions to practise first

The questions the board asked again come first, most asked first. Each one says how often and when.

Question 1
Asked 3 times: 2023*, 2025*, 2026 (* = numbers or wording changed that year)
9 $A(4a, 3a)$
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Question 2
Asked 3 times: 2023*, 2024*, 2026 (* = numbers or wording changed that year)
2 $P(-4, -2)$
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Question 3
Asked 3 times: 2023, 2025, 2026* (* = numbers or wording changed that year)
23 $(x - 7, 2x)$
Question 4
Asked 3 times: 2023*, 2024, 2025 (* = numbers or wording changed that year)
23 $A(7, 1)$
Question 5
Asked 2 times: 2024, 2026
21 $(1, 0)$
Question 6
Asked 2 times: 2024*, 2026 (* = numbers or wording changed that year)
15 $(a\cos\theta + b\sin\theta, 0)$
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Question 7
Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)
8 $(5, -4)$
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Question 8
Asked 2 times: 2025*, 2026 (* = numbers or wording changed that year)
23 $A(4, 5)$
Question 9
Asked 2 times: 2024*, 2025 (* = numbers or wording changed that year)
25 $\Delta ABC$
Question 10
Asked 2 times: 2023, 2025
16 $(2, 4)$
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7.2 Distance Formula

Solved Examples

Exercise 7.1

7.3 Section Formula

Solved Examples

Exercise 7.2

What the board has asked from this chapter

2026

2025

2024

2023

The 10 board questions to practise first

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10