**Download NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.2 – Coordinate Geometry**

**1. Find the coordinates of the point which divides the join of (-1, 7) and (4, -3) in the ratio 2:3.**

Using section formula

x = = = = 1

y = = = = 3

Therefore, the coordinates of the point are (1, 3).

**2. Find the coordinate of the points of trisection of the line segment joining (4, -1) and (-2, -3).**

Let **A** and **B** denote the points (4, -1) and (-2, -3) respectively and **P** and **Q** be the points of trisection of the line segment **AB** such that **P** is closer to **A** and **Q** is closer to **B
∴ **AP = PQ = QB …(i)

Ratio in which P divides AB = =

= (Substituting values from equation (i))

= = 1:2

Similarly, the ratio in which Q divides AB = 1:2

∴ Coordinates of P =

=

=

=

Coordinates of Q =

=

=

=

**3. To conduct Sports Day activities, in your rectangular shaped school ground ABCD, lines have been drawn with chalk powder at a distance of 1 m each. 100 flower pots have been placed at a distance of 1 m from each other along AD, as shown in the figure. Niharika runs th the distance AD on the 2 ^{nd} line and posts a green flag. Preet runs th the distance AD on the eighth line and posts a red flag. What is the distance between both the flags? If Rashmi has to post a blue flag exactly halfway between the line segments joining the two flags, where should she post her flag?**

Assume a coordinate system fixed in the ground **ABCD** with **A** as origin, **AB** as x-axis and **AD** as y-axis

∵ Niharika runs on 2^{nd} line

∴ x-coordinate of Niharika = 2 m

∵ Preet runs on 8^{nd} line

∴ x-coordinate of Preet = 8 m

∵ Niharika posts the green flag after running of the AD

∴ y-coordinate of green flag = = = 25 m

∵ Preet posts the red flag after running of the AD

∴ y-coordinate of red flag = = = 20 m

Coordinates of green flag = (2, 25)

Coordinates of red flag = (8, 20)

Using distance formula

Distance between the two flags

=

=

=

=m

∵ Blue flag has to be posted mid-way between the red and green flag

∴ The coordinates of blue flag will be the coordinates of mid-point of the line segment joining the green and red flag

Using section formula

Coordinates of blue flag

=

=

= (5, 22.5)

Therefore, the blue flag has to be posted on the 5^{th} line at a distance of 22.5 m from the line AB.

**4. Find the ratio in which the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6).**

Let the line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6) in the ratio **m:1**∴ (-1, 6) =

From x-coordinate

-1 =

-m – 1 = -3 + 6m

3 – 1 = 7m

m =

From y-coordinate

6 =

6m + 6 = 10 – 8m

14m = 4

m =

Therefore, line segment joining the points (-3, 10) and (6, -8) is divided by (-1, 6) in the ratio 2:7

**5. Find the ratio in which the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis. Also find the coordinates of the point of division.**

Let the line segment joining **A**(1, -5) and **B**(-4, 5) is divided by the point **P**(x, y) in the ratio **m:1**∴(x,y)=…(i)

∵ P lies on x-axis

∴ y-coordinate = 0

= 0

-5 + 5m = 0

5m = 5

m=1

Putting value in equation (i)

(x, y) =

(x, y) =

(x, y) =

Therefore, the line segment joining A(1, -5) and B(-4, 5) is divided by the x-axis at the point ( , 0) in 1:1

**6. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.**

Let **A**, **B**, **C** and **D** denote the points (1, 2), (4, y), (x, 6) and (3, 5) respectively.

∵ Diagonals of a parallelogram bisect each other

∴ Coordinates mid-point of AC = Coordinates of mid-point of BD

=

=

From the x-coordinate

=

1 + x = 7

x = 6

From y-coordinate

=

8 = 5 + y

y = 3

Therefore, the values of x is 3 and y is 6.

**7. Find the coordinates of a point A, where AB is the diameter of a circle whose centre is (2, -3) and B is (1, 4).**

Let the coordinates of A be (x, y)

∵ AB is the diameter

∴ The centre of the circle is the mid-point of the line segment joining A and B

Using section formula

(2, -3) =

2 =

4 = x + 1

x = 3

-3 =

-6 = y + 4

y = -10

Therefore, the coordinates of A are (3, -10)

**8. If A and B are (-2, -2) and (2, -4), respectively, find the coordinates of P such that AP = AB and P lies on the line segment AB.**

Given, AP = AB …(i)

AP + PB = AB

PB = AB – AP

PB = AB – AB (From equation (i))

PB = AB

The ratio in which P divides the line segment AB = = =

Using section formula

P =

=

=

Therefore, the coordinates of P are

**9. Find the coordinates of the points which divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts.**

Let **P**, **Q** and **R** be the points which divide the line segment AB into four equal parts

∴ AP = PQ = QR = RB …(i)

Ratio in which Q divides AB = =

= (From equation (i))

= 1

∴ Q is the mid-point of line segment AB

Q = (Using section formula)

=

= (0, 5)

Ratio in which P divides AQ =

= (From equation (i))

= 1

∴ P is the mid-point of line segment AQ

Similarly, R is the mid-point of QB

∴ P = = (Using section formula)

R = = (Using section formula)

The coordinates of the points that divide the line segment joining A(-2, 2) and B(2, 8) into four equal parts are (-1, ), (0, 5) and (1, ).

**10. Find the area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order.**

Let **A**, **B**, **C **and **D** denote the points (3, 0), (4, 5), (-1, 4) and (-2, -1) respectively

Length of diagonals

AC = = = =

BD = = = =

Area of rhombus = ×(Product of length of diagonals)

= ×AC×BD

=

=

= 24 sq. units

**Download NCERT Solutions For Class 10 Maths Chapter 7 Exercise 7.2 – Coordinate Geometry**

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