Class 9 MAHARASHTRA STATE TEXTBOOK BUREAU Solutions Maths Chapter 7 - Co-ordinate Geometry
Co-ordinate Geometry Exercise 7.1
Solution 1
Solution 2
i. Quadrant I
ii. Quadrant III
iii. Quadrant IV
iv. Quadrant II
Solution 3
Co-ordinate Geometry Exercise 7.2
Solution 1
d(O, A) = 3 cm, d(A, B) = 3 cm, d(B, C) = 3 cm, d(O, C) = 3 cm and each angle of OABC is 90°
∴ OABC is a square.
Solution 2
The equation of a line parallel to the Y-axis is x = a.
Since, the line is at a distance of 7 units to the left of Y-axis,
∴ a = -7
∴ x = -1 is the equation of the required line.
Solution 3
The equation of a line parallel to the X-axis is y = b.
Since, the line is at a distance of 5 units below the X-axis.
∴ b = -5
∴ y = -5 is the equation of the required line.
Solution 4
The equation of a line parallel to the Y-axis is x = a.
Here, a = -3
∴ x = -3 is the equation of the required line.
Solution 5
Equation of Y-axis is x = 0.
Equation of the line parallel to the Y-axis is x = - 4. … [Given]
∴ Distance between the Y-axis and the line x = - 4 is 0 - (- 4) … [0 > -4]
= 0 + 4 = 4 units
∴ The distance between the Y-axis and the line x = - 4 is 4 units.
Solution 6
i. The equation of a line parallel to the Y-axis is x = a.
∴ The line x = 3 is parallel to the Y-axis.
ii. y - 2 = 0
∴ y = 2
The equation of a line parallel to the X-axis is y = b.
∴ The line y - 2 = 0 is parallel to the X-axis.
iii. x + 6 = 0
∴ x = -6
The equation of a line parallel to the Y-axis is x = a.
∴ The line x + 6 = 0 is parallel to the Y-axis.
iv. The equation of a line parallel to the X-axis is y = b.
∴ The line y = - 5 is parallel to the X-axis.
Solution 7
From the graph, the line drawn intersects the X-axis at D(5, 0) and the Y-axis at C(0, 5).
Solution 8
x + 4 = 0
∴ x = - 4
y - 1 = 0
∴ y = 1
2x + 3 = 0
∴2x = -3
∴ x = -1.5
3y - 15 = 0
3y = 15
∴ y = 5
The co-ordinates of the point of intersection of x + 4 = 0 and y - 1 = 0 are A(-4, 1).
The co-ordinates of the point of intersection of y - 1 = 0 and 2x + 3 = 0 are B(-1.5, 1).
The co-ordinates of the point of intersection of 3y - 15 = 0 and 2x + 3 = 0 are C(-1.5, 5).
The co-ordinates of the point of intersection of x + 4 = 0 and 3y - 15 = 0 are D(-4, 5).
Solution 9
i. x + y = 2
∴ y = 2 - x
When x = 0,
y = 2 - x
= 2 - 0
= 2
When x = 1,
y = 2 - x
= 2 - 1
= 1
When x = 2,
y = 2 - x
= 0
ii. 3x - y = 0
∴ y = 3x
When x = 0,
y = 3x
= 3(0)
= 0
When x = 1,
y = 3x
= 3(1)
= 3
When x = -1,
y = 3x
= 3(-1)
= -3
iii. 2x + y = 1
∴ y = 1 - 2x
When x = 0,
y = 1 - 2x
= 1 - 2(0)
= 1 - 0 = 1
When x = 1,
y = 1 - 2x
= 1- 2(1)
= 1 - 2
= -1
When x = -1,
y = 1 - 2x
= 1 - 2(-1)
= 1 + 2
= 3
Co-ordinate Geometry Exercise Problem Set 7
Solution 1(i)
(C) (α, o)
Solution 1(ii)
(A) (α, α)
Solution 1(iii)
(B) y = 0
Solution 1(iv)
(C) Third
Solution 1(v)
The y co-ordinate of all the points is the same.
∴ The line which passes through the given points is parallel to X-axis.
(C) Parallel to X-axis
Solution 1(vi)
(B) Q and R
Solution 2
i. Q(-2, 2) and R(4, -1)
ii. T(0, -1) and M(3, 0)
iii. Point S lies in the third quadrant.
iv. The x and y co-ordinates of point O are equal.
Solution 3
Solution 4
Solution 5
i. Distance of line LM from the Y-axis is 3 units.
ii. P(3, 2), Q (3, -1), R(3, 0)
iii. x co-ordinate of point L = 3
x co-ordinate of point M = 3
∴ Difference between the x co-ordinates of the points L and M = 3 - 3= 0
Solution 6
The equation of a line parallel to the X-axis is y = b.
There are 2 lines which are parallel to X-axis and at a distance of 5 units.
Their equations are y = 5 and y = -5.
Solution 7
Equation of Y-axis is x = 0.
Since, 'α' is a real number, there are two possibilities.
Case I: α > 0
Case II: α < 0 ∴ Distance between the Y-axis and the line x = α = α - 0 = α
Since, |α| = α, α > 0
= - α, α < 0
∴ Distance between the Y-axis and the line x = α is |α|.
