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.

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(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.

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(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

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(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.

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(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.

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(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 ?

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( $8 \sqrt{2}$ )

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’.

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(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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2

3

4

(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)

1

2

3

4

(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?

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

1

2

3

4

(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

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

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.

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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.

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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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