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RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2

July 20, 2021 by Fazal Leave a Comment

RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 is part of RBSE Solutions for Class 10 Maths. Here we have given Rajasthan Board RBSE Class 10 Maths Chapter 9 Co-ordinate Geometry Exercise 9.2.

Rajasthan Board RBSE Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2

Question 1.
Find the co-ordinates of the point which divides the line (RBSESolutions.com) segment joining the points (3, 5) and (7, 9) in the ratio 2 : 3 internally.
Solution :
Let point P(x, y) divides the line segment joining the point A(3, 5) and B(7, 9) internally in the ratio 2 : 3.
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 1
Hence, the coordinate of P is \(\left( 4\frac { 3 }{ 5 } ,6\frac { 3 }{ 5 } \right) \).

RBSE Solutions

Question 2.
Find the co-ordinates of the point which (RBSESolutions.com) divides the line segment joining the points (5, -2) and \(\left( -1\frac { 1 }{ 2 } ,4 \right) \) in the ratio 7 : 9 externally.
Solution :
Let point P(x, y) divides the line segment joining the points A(5, -2) and B\(\left( -1\frac { 1 }{ 2 } ,4 \right) \) externaly in the ratio 7 : 9.
x1 = 5      y1 = -2         m1 = 7
x2 = -1\(\frac { 1 }{ 2 }\)    y2 = 4    m2 = 9
By formula of external division
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 2
Hence, the coordinate of P is \(\left( 27\frac { 3 }{ 4 } ,-23 \right) \)

Question 3.
Prove that origin O divides the line joining (RBSESolutions.com) the points 4(1, -3) and B(-3, 9) in the ratio 1 : 3 internally. Find the co-ordinates of the points which externally divides the line.
Solution :
Let the point P(x, y) divides the line segment joining the point A(1, -3) and B(-3, 9) internally in the ratio 1 : 3.
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 3
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 4
Hence co-ordinate of P(x, y) is (0, 0). So origin O is divides (RBSESolutions.com) the line segment joining the given points internally in the ratio 1 : 3.
Again point P(x, y) divides externally, then by formula of external division
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 5
Hence, co-ordinate of point P which divides externally = (3, -9).

Free Distance and Midpoint Calculator calculates the distance and midpoint between two points instantaneously.

Question 4.
Find the mid point of line joining (RBSESolutions.com) the points (22, 20) and (0, 16).
Solution :
Let co-ordinates of mid point is P (x, y) which ¡s line joining the points A(22, 20) and B(0, 16).
x1 = 22, y1 = 20,  x2 = 0, y2 = 16
By formula of mid point
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 6
Hence, co-ordinate of mid point P(x, y) = (11, 18)

Question 5.
In which ratio, x-axis divides the line segment (RBSESolutions.com) which joins points (5, 3) and (-3, -2)?
Solution :
On x-axis, the ordinate of each point is zero. So let point P(x, 0) divides the line segment joining the points A(5, 3) and B(-3, -2) internally in the ratio m1 : m2
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 7
Hence, line segment joining the given points by x-axis divides internally in the ratio 3 : 2.

Question 6.
In which ratio, y-axis, divides the line (RBSESolutions.com) segment which joins points (2, -3) and (5, 6)?
Solution :
On y-axis, coordinate of point x is zero, so let point P(0, y) divides the line segment joining the point A(2, -3) and B(5, 6) externally in the ratio m1 : m2.
Then by formula of external division
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 8
⇒ 5m1 – 2m2 = 0
⇒ 5m1 = 2m2
⇒ \(\frac { { m }_{ 1 } }{ { m }_{ 2 } } =\frac { 2 }{ 5 } \)
⇒ m1 : m2 = 2 : 5
Hence, line segment joining these points divides externally in the ratio 2 : 5 by y-axis.

RBSE Solutions

Question 7.
In which ratio, point (11, 15) divides the (RBSESolutions.com) line segment which joins (15, 5) and (9, 20)?
Solution :
Let the point P(1 1, 15) divides the line segment joining the point A(15, 5) and B(9, 20) internally in the ratio λ : 1
Hence x1 = 15    y1 = 5         m1 = λ
x2 = 9      y2 = 20       m2 = 1
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 9
⇒ 11(λ + 1) = 9λ + 15
⇒ 11λ + 11 = 9λ + 15
⇒ 11λ – 9λ = 15 – 11
⇒ 2λ = 4
λ = \(\frac { 4 }{ 2 }\) = \(\frac { 2 }{ 1 }\)
∴ λ : 1 = 2 : 1
Hence, required ratio is 2 : 1.

Question 8.
If point P (3, 5) divides line segment which (RBSESolutions.com) joins A(-2, 3) and B(x, y) in the ratio 4 : 7 internally, then find the co-ordinates of B.
Solution :
Let the coordinate of point B is (x, y)
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 10
Let the point P(3, 5) divides the line segment joining the points A(-2, 3) and B(x, y) internally in the inthe ratio 4 : 7.
So, x1 = -2,     y1 = 3       m1 = 4
x2 = x       y2 = y        m2 = 7
By section formula
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 11
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 12
Hence, the co-ordinate of point B is \(\left( \frac { 47 }{ 4 } ,\frac { 17 }{ 2 } \right)\)

Question 9.
Find the co-ordinates of point which (RBSESolutions.com) trisects the line joining point (11, 9) and (1, 2).
Solution :
Let P(x1 y1) and Q(x2, y2) are required points which is trisect the line segment joining the points A(11, 9) and B(1, 2) respectively.
Let AP = PQ = BQ = x
PB = x + x = 2x
AQ = x + x = 2x
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 13
Hence point P divides line segment AB in the (RBSESolutions.com) ratio 1 : 2 and point Q, divides the line segment Ab in the ratio 2 : 1.
By the section formula for point P,
m1 = 1, m2 = 2
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 14
∴ Hence the co-ordinate of point P is \(\left( \frac { 23 }{ 3 } ,\frac { 20 }{ 3 } \right)\)
for point Q,
m1 = 2, m2 = 1
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 15
So, the co-ordinate of Q = \(\left( \frac { 13 }{ 3 } ,\frac { 13 }{ 3 } \right)\)
Hence, required coordinate of point P and Q is \(\left( \frac { 23 }{ 3 } ,\frac { 20 }{ 3 } \right)\) and \(\left( \frac { 13 }{ 3 } ,\frac { 13 }{ 3 } \right)\) respectively.

Question 10.
Find the co-ordinates of point which quarter (RBSESolutions.com) sects the line joining point (-4, 0) and (0, 6).
Solution :
Let C, D and E are required point which quarter sects the line segment joining the points A(-4, 0) and B(0, 6)
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 16
Since D is mid point of A and B, C is is midpoint A and D, and E ¡s mid point of D and B, then AC = CD = DE = EB
Now, co-ordinate of mid point D of A and B.
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 17
= \(\left( \frac { -2 }{ 2 } ,\frac { 9 }{ 2 } \right)\)
= \(\left( -1,\frac { 9 }{ 2 } \right)\)
Hence, co-ordinate of points divided in four equal (RBSESolutions.com) part of AB are \(\left( -3,\frac { 3 }{ 2 } \right)\), (-2, 3) and \(\left( -1,\frac { 9 }{ 2 } \right)\) respectively.

RBSE Solutions

Question 11.
Find the ratio in which line 3x + y = 9 divides the line segment which joins points (1, 3) and (2, 7)
Solution :
Let the line 3x + y = 9 divides the line segment joining A(1, 3) and B(2, 7) at point P(x, y) in the ratio λ : 1
x1 = 1     y 1 = 3     m1 = λ
x2 = 2     y2 = 7      m2 = 1
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 18
⇒ 6λ + 3 + 7λ + 3 = 9(λ + 1)
⇒ 13λ + 6 = 9λ + 9
⇒ 13λ – 9λ = 9 – 6
⇒ 4λ = 3
⇒ λ = \(\frac { 3 }{ 4 }\)
λ : 1 = 3 : 4
Hence, required ratio is 3 : 4.

Question 12.
Find the ratio where point (-3, P), divides internally (RBSESolutions.com) the line segment which joins points (-5, -4) and (-2, 3). Also find P.
Solution :
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 19
Let the point P(-3, p) divides the line segment joining the points A(-5, -4) and B(-2, 3) internally in the ratio m1 : m2.
Hence, x co-ordinate of point P(-3, p)
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 20
= -3(m1 + m2) = -2m1 – 5m2
⇒ -3m1 – 3m2 = -2m1 – 5m2
⇒ -3m1 + 2m1 = -5m2 + 3m2
⇒ – m1 = -2m2
⇒ \(\frac { { m }_{ 1 } }{ { m }_{ 2 } } =\frac { -2 }{ -1 } \) = \(\frac { 2 }{ 1 }\)
Hence required ratio m1 : m2 = 2 : 1
Now, y co-ordinate of point P(-3, p)
RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 21
Hence, required (RBSESolutions.com) ratio 2 : 1 and p = \(\frac { 2 }{ 3 }\)

RBSE Solutions

We hope the given RBSE Solutions for Class 10 Maths Chapter 9 Co-ordinate Geometry Ex 9.2 will help you. If you have any query regarding Rajasthan Board RBSE Class 10 Maths Chapter 9 Co-ordinate Geometry Exercise 9.2, drop a comment below and we will get back to you at the earliest.

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