Class 10 Maths Coordinate Geometry questions with solutions

Q 1 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Find the distance between points A and B.

(5.6)

Distance between A(1, 9) and B(5, 13) is

$= \sqrt{{(5 - 1)}^{2} + {(13 - 9)}^{2}} = \sqrt{16 + 16} = \sqrt{32} = 4 \sqrt{2} = 5.6 units$

Q 2 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Write the co-ordinates of the mid point of line segment joining points M and Q.

(7,7)

Midpoint of the line segment joining M(5, 11) and Q(9, 3) is given by

$(\frac{5 + 9}{2}, \frac{11 + 3}{2}) = (\frac{14}{2}, \frac{14}{2}) = (7, 7)$

Q 3 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Find the coordinates of H, G and also find the distance between them

(5.6)

As per graph the coordinate of H is (1, 5) and of G is (5, 1).

Distance $H G = \sqrt{{(5 - 1)}^{2} + {(1 - 5)}^{2}} = \sqrt{16 + 16} = \sqrt{32} = 4 \sqrt{2} = 5.6 units$

Q 4 :

Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of the city from where bank, hospital, post office and supermarket can be easily accessed. In the graph, the bank is plotted as A(9, 5), hospital as B(– 3, – 1) and supermarket as C(5, – 5) such that A, B, C form a triangle.

Based on the above given information, answer the question :

Q. Find the distance between the bank and the hospital.

(13.416)

Distance between bank and hospital $= \sqrt{{(- 3 - 9)}^{2} + {(- 1 - 5)}^{2}} = \sqrt{144 + 36}$

$= \sqrt{180}$ units or $6 \sqrt{5}$ units = 13.416

Q 5 :

Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of the city from where bank, hospital, post office and supermarket can be easily accessed. In the graph, the bank is plotted as A(9, 5), hospital as B(– 3, – 1) and supermarket as C(5, – 5) such that A, B, C form a triangle.

Based on the above given information, answer the question :

Q. In between the bank and the supermarket, there is a post office plotted at E which is their mid-point. Find the coordinates of E.

(7,0)

Coordinates of E are $(\frac{9 + 5}{2}, \frac{- 5 + (- 5)}{2}) = (7, 0)$

Q 6 :

Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of the city from where bank, hospital, post office and supermarket can be easily accessed. In the graph, the bank is plotted as A(9, 5), hospital as B(– 3, – 1) and supermarket as C(5, – 5) such that A, B, C form a triangle.

Based on the above given information, answer the question :

Q. In between the hospital and the supermarket, there is a bus stop plotted as D, which is their mid-point. If Partha wants to reach the bus stand from the bank, then how much distance does he need to cover ?

( $8 \sqrt{2}$ )

Coordinates of D are $(\frac{- 3 + 5}{2}, \frac{- 1 + (- 5)}{2}) = (1, - 3)$

Distance Partha need to cover $= \sqrt{{(9 - 1)}^{2} + (5 - {(- 3))}^{2}} = \sqrt{64 + 64} = \sqrt{128}$ units or $8 \sqrt{2}$ units

Q 7 :

Partha, a software engineer, lives in Jerusalem for his work. He lives in the most convenient area of the city from where bank, hospital, post office and supermarket can be easily accessed. In the graph, the bank is plotted as A(9, 5), hospital as B(– 3, – 1) and supermarket as C(5, – 5) such that A, B, C form a triangle.

Based on the above given information, answer the question :

Q. P and Q are two different garment shops lying between the bank and the hospital, such that BP = PQ = QA. If the coordinates of P and Q are (1, a) and (b, 3) respectively, then find the values of ‘a’ and ‘b’.

(a = 1, b = 5)

P is mid-point of BQ

$∴$ $a = \frac{- 1 + 3}{2} = 1$

Q is mid-point of PA

$∴$ $b = \frac{1 + 9}{2} = 5$

Q 8 :

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD. 100 flowerpots have been placed at a distance of 1 m from each other along AD as shown in the given figure below.

Niharika runs 1/4 of the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 of the distance ADon the eighth line and posts a red flag.

Based on the above information answer the following questions:

(i) Find the position of green flag.

(2, 25)
(2, 24)
(3, 25)
(2, 15)

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(1)

Since Niharika runs 1/4 of the distance AD on the second line and posts a green flag,

$Coordinates of green flag = (2, \frac{100}{4}) = (2, 25)$

Q 9 :

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD. 100 flowerpots have been placed at a distance of 1 m from each other along AD as shown in the given figure below.

Niharika runs 1/4 of the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 of the distance ADon the eighth line and posts a red flag.

Based on the above information answer the following questions:

(ii) Find the position of red flag.

(8, 15)
(8, 20)
(8, 25)
(8, 10)

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(2)

Since Preet runs 1/5of the distance AD on the eighth line and posts a red flag

$Coordinates of red flag = (8, \frac{100}{5}) = (8, 20)$

Q 10 :

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD. 100 flowerpots have been placed at a distance of 1 m from each other along AD as shown in the given figure below.

Niharika runs 1/4 of the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 of the distance ADon the eighth line and posts a red flag.

Based on the above information answer the following questions:

(iii) (a) If Rashmi has to post a blue flag exactly halfway between the line segment joining the two flags, where should she post her flag?

$(5, \frac{44}{2})$
$- (5, \frac{45}{2})$
$(5, \frac{45}{3})$
$(5, \frac{45}{2})$

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(4)

We have the line joining the two flags (shown).

Let B be the position of the blue flag posted by Rashmi, which is the midpoint of

$G (2, 25) a n d R (8, 20) . I t s c o o r d i n a t e s : B = (\frac{8 + 2}{2}, \frac{20 + 25}{2}) = (\frac{10}{2}, \frac{45}{2}) = (5, \frac{45}{2})$

Q 11 :

In order to conduct Sports Day activities in your School, lines have been drawn with chalk powder at a distance of 1 m each, in a rectangular shaped ground ABCD. 100 flowerpots have been placed at a distance of 1 m from each other along AD as shown in the given figure below.

Niharika runs 1/4 of the distance AD on the 2nd line and posts a green flag. Preet runs 1/5 of the distance ADon the eighth line and posts a red flag.

Based on the above information answer the following questions:

(iii) (b) If Joy has to post a flag at one-fifth distance from green flag in the line segment joining the green and red flags, then where should he post his flag?

$F = (\frac{16}{5}, 24)$
$F = (\frac{16}{5}, 21)$
$F = (\frac{- 16}{5}, 24)$
$F = (\frac{16}{2}, 24)$

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(1)

Let the coordinates of the flag F, posted by Joy, be F(x,y).

Using section formula (internal),
Joy posts the flag at one-fifth of the distance from the green flag towards the red flag:

$x = \frac{1 \cdot 8 + 4 \cdot 2}{1 + 4} = \frac{8 + 8}{5} = \frac{16}{5} y = \frac{1 \cdot 20 + 4 \cdot 25}{1 + 4} = \frac{20 + 100}{5} = \frac{120}{5} = 24 T h u s, F = (\frac{16}{5}, 24)$

Q 12 :

Shown below is a map of Giri’s neighbourhood. 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 of 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.

Based on the above information, answer the following questions:

(i) What is the x-coordinate of the mall’s location?

0
1
2
4

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(1)

Since the distance between the hotel (H) and the mall (M) is half of the distance between the mall and the main gate (Mg):

$\frac{M g M}{M H} = \frac{2}{1} \Rightarrow M g M : M H = 2 : 1$

Using section formula, coordinates of mall M(x,y) are given by:

$x = \frac{2 \times (- 2) + 1 \times 4}{2 + 1}, y = \frac{2 \times 5 + 1 \times 17}{2 + 1} \Rightarrow x = 0, y = \frac{27}{3} = 9$

Thus, x-coordinate of mall is 0.

Q 13 :

Shown below is a map of Giri’s neighbourhood. 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 of 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.

Based on the above information, answer the following questions:

(ii) What are the coordinates of the fire station?

(4, 2)
(4, 1)
(3, 2)
-(4, 2)

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(2)

Let the coordinates of the fire station be (x,y)

Since the bus stand is exactly midway between the main gate of the garden and the fire station, using midpoint formula:

$(\frac{x + 4}{2}, \frac{y + 17}{2}) = (4, 9) \Rightarrow \frac{x + 4}{2} = 4, \frac{y + 17}{2} = 9 \Rightarrow x + 4 = 8, y + 17 = 18 \Rightarrow x = 4, y = 1 H e n c e, c o o r d i n a t e s o f t h e f i r e s t a t i o n a r e (4, 1) .$

Q 14 :

Shown below is a map of Giri’s neighbourhood. 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 of 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.

Based on the above information, answer the following questions:

(iii) (a) What is the shortest distance between the water tank and the school?

13 units
15 units
11 units
10 units

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(1)

Coordinates of water tank and school are: $W (10, 9) and S 22, 14)$

Shortest distance between them: $W S = \sqrt{(22 - 10)^{2} + (14 - 9)^{2}} = \sqrt{144 + 25} = \sqrt{169} = 13 units$

Q 15 :

Shown below is a map of Giri’s neighbourhood. 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 of 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.

Based on the above information, answer the following questions:

(iii) (b) How much more is the shortest distance of the school from the water tank than the distance of the school from the police station?

5 units
6 units
3 units
2 units

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(2)

Coordinates of police station are P(22,7)

Distance of police station from school:.

$S P = \sqrt{(22 - 22)^{2} + (14 - 7)^{2}} = \sqrt{0^{2} + 7^{2}} = 7 units Difference in distances : 13 - 7 = 6 units$

Q 16 :

Two friends, Seema and Aditya, work in the same office in Delhi. For the Christmas vacation, they both decided to travel to their hometowns, represented by Town A and Town B in the figure shown. Town A and Town B are connected by trains departing from the same station, Station C, in Delhi.

Based on the above information, answer the following questions:

(i) Who will travel more distance, Seema or Aditya, to reach their hometown?

Aditya
Seema
all of these
none of the above

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(1)

Distance travelled by Seema: $C A = \sqrt{(- 5 - 2)^{2} + (4 - 6)^{2}} = \sqrt{49 + 4} = \sqrt{53} units$

Distance travelled by Aditya: $C B = \sqrt{(5 + 5)^{2} + (2 - 4)^{2}} = \sqrt{100 + 4} = \sqrt{104} units$

Clearly, Aditya travels more distance.

Q 17 :

Two friends, Seema and Aditya, work in the same office in Delhi. For the Christmas vacation, they both decided to travel to their hometowns, represented by Town A and Town B in the figure shown. Town A and Town B are connected by trains departing from the same station, Station C, in Delhi.

Based on the above information, answer the following questions:

(ii) Seema and Aditya planned to meet at a location D situated at the mid-point of the line joining the points represented by Town A and Town B. Find the coordinates of the point represented by D.

Given:

$T o w n A = A (2, 6) T o w n B = B (5, 2) S t a t i o n C = C (- 5, 4)$

$(\frac{7}{2}, 3)$
$(\frac{7}{2}, 4)$
$(\frac{- 7}{2}, 4)$
$(\frac{6}{3}, 4)$

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(2)

Since D is the midpoint of AB:

Coordinates of D:

$D = (\frac{2 + 5}{2}, \frac{6 + 2}{2}) = (\frac{7}{2}, 4) T h u s, (\frac{7}{2}, 4) i s t h e l o c a t i o n o f p o i n t D .$

Q 18 :

A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at a 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 them.

In the above situation, the gardener took help from class 10 students. They made a chart for it, which looks like the given figure

Based on the above information, answer the following questions:

(i) If A is taken as origin, what are the coordinates of the vertices of $Δ P Q R ?$

P(4, 6), Q(3, 2), R(6, 5).
P(3, 6), Q(4, 2), R(6, 5).
P(5 6), Q(3, 2), R(6,3).
P(4, 2), Q(3, 4), R(6, 5).

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(1)

If A is taken as origin, then coordinates of the vertices of ΔPQR are:
P(4, 6), Q(3, 2), R(6, 5).

Finding distances PQ and QR

$P Q = \sqrt{(3 - 4)^{2} + (2 - 6)^{2}} = \sqrt{1 + 16} = \sqrt{17} R = \sqrt{(6 - 3)^{2} + (5 - 2)^{2}} = \sqrt{9 + 9} = \sqrt{18} = 3 \sqrt{2}$

Q 19 :

A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at a 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 them.

In the above situation, the gardener took help from class 10 students. They made a chart for it, which looks like the given figure

Based on the above information, answer the following questions:

(ii) (a) Find distances PQ and QR.

$P Q = \sqrt{17} Q R = 3 \sqrt{2}$
$P Q = \sqrt{16} Q R = - 3 \sqrt{2}$
$P Q = \sqrt{17} Q R = 3 \sqrt{4}$
$P Q = - \sqrt{17} Q R = 1 \sqrt{2}$

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(1)

We have P(4, 6), Q(3, 2) and R(6, 5)

Finding distances PQ and QR

$P Q = \sqrt{(3 - 4)^{2} + (2 - 6)^{2}} = \sqrt{1 + 16} = \sqrt{17} R = \sqrt{(6 - 3)^{2} + (5 - 2)^{2}} = \sqrt{9 + 9} = \sqrt{18} = 3 \sqrt{2}$

Q 20 :

A national park is an area set aside by the government to preserve and protect the natural environment

The graph below shows a map of a National Park. The shaded areas indicate woods. The plain areas indicate meadows and fields without trees. Point O on the graph represents the location of the park’s supervisor’s office, and points P and Q are the ranger’s towers

(i) Find the distance between the towers P(0, 7.5) and Q(–15, 15).

16.77 units
15.77 units
12.77 units
16.67 units

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(1)

$(i) D i s \tan c e b e t w e e n t o w e r s P a n d Q : P Q = \sqrt{(- 15 - 0)^{2} + (15 - 7.5)^{2}} = \sqrt{(- 15)^{2} + (7.5)^{2}} = \sqrt{225 + 56.25} = \sqrt{281.25} = 16.77 units$

Q 21 :

A national park is an area set aside by the government to preserve and protect the natural environment.

The graph below shows a map of a National Park. The shaded areas indicate woods. The plain areas indicate meadows and fields without trees. Point O on the graph represents the location of the park’s supervisor’s office, and points P and Q are the ranger’s towers.

(ii) Find the distance of the point S(5, 25) from the x-axis.

30 units
25 units
20 units
22 units

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(2)

The distance of point S(5, 25) from x-axis is simply its y-coordinate (absolute value): = 25 units

Topic Question Set

Q 1 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Find the distance between points A and B.

Q 2 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Write the co-ordinates of the mid point of line segment joining points M and Q.

Q 3 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Find the coordinates of H, G and also find the distance between them

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Topic Question Set

Q 1 : The top of a table is shown in the figure given below: On the basis of above information answer the following questions. Q. Find the distance between points A and B.

Q 2 : The top of a table is shown in the figure given below: On the basis of above information answer the following questions. Q. Write the co-ordinates of the mid point of line segment joining points M and Q.

Q 3 : The top of a table is shown in the figure given below: On the basis of above information answer the following questions. Q. Find the coordinates of H, G and also find the distance between them

Want Us to Email you About Special Offers & Updates?

Q 1 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Find the distance between points A and B.

Q 2 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Write the co-ordinates of the mid point of line segment joining points M and Q.

Q 3 :

The top of a table is shown in the figure given below:

On the basis of above information answer the following questions.

Q. Find the coordinates of H, G and also find the distance between them