# Co-Ordinate Geometry

Chapters

- ap-scert-9th-class-Maths-Lesson-1-Real-Numbers
- ap-scert-9th-class-Maths-Lesson-2-Polynomials-and-Factorisation
- ap-scert-9th-class-Maths-Lesson-3-The-Elements-of-Geometry
- ap-scert-9th-class-Maths-Lesson-4-Lines-and-Angles
- ap-scert-9th-class-Maths-Lesson-5-Co-Ordinate-Geometry
- ap-scert-9th-class-Maths-Lesson-6-Linear-Equation-in-Two-Variables
- ap-scert-9th-class-Maths-Lesson-7-Triangles
- ap-scert-9th-class-Maths-Lesson-8-Quadrilaterals
- ap-scert-9th-class-Maths-Lesson-9-Statistics
- ap-scert-9th-class-Maths-Lesson-10-Surface-Areas-and-Volumes
- ap-scert-9th-class-Maths-Lesson-11-Areas
- ap-scert-9th-class-Maths-Lesson-12-Circles
- ap-scert-9th-class-Maths-Lesson-13-Geometrical-Constructions
- ap-scert-9th-class-Maths-Lesson-14-Probability
- ap-scert-9th-class-Maths-Lesson-15-Proofs-in-Mathematics

- ap-scert-9th-class-Maths-Lesson-1-Real-Numbers
- ap-scert-9th-class-Maths-Lesson-2-Polynomials-and-Factorisation
- ap-scert-9th-class-Maths-Lesson-3-The-Elements-of-Geometry
- ap-scert-9th-class-Maths-Lesson-4-Lines-and-Angles
- ap-scert-9th-class-Maths-Lesson-5-Co-Ordinate-Geometry
- ap-scert-9th-class-Maths-Lesson-6-Linear-Equation-in-Two-Variables
- ap-scert-9th-class-Maths-Lesson-7-Triangles
- ap-scert-9th-class-Maths-Lesson-8-Quadrilaterals
- ap-scert-9th-class-Maths-Lesson-9-Statistics
- ap-scert-9th-class-Maths-Lesson-10-Surface-Areas-and-Volumes
- ap-scert-9th-class-Maths-Lesson-11-Areas
- ap-scert-9th-class-Maths-Lesson-12-Circles
- ap-scert-9th-class-Maths-Lesson-13-Geometrical-Constructions
- ap-scert-9th-class-Maths-Lesson-14-Probability
- ap-scert-9th-class-Maths-Lesson-15-Proofs-in-Mathematics

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Solutions

In a locality, there is a main road along North - South direction. The map is given below. With the help of the picture answer the following questions.

- i) What is the 3rd object on the left side in street no. 3 while going in east direction ?
- ii) Find the name of the 2nd house which is on right side of street 2 while going in east direction.
- iii) Locate the position of Mr. K’s house.
- iv) How do you describe the position of the post office ?
- v) How do you describe the location of the hospital ?
- Solution:
- i) Water tank
- ii) Mr. J’s house
- iii) In street No. 2, 3rd house on right side.
- iv) In street No. 4, the first house on right side.
- v) In street No. 4, the last house on left side.

Write the quadrant in which the following points lie.

- i) (- 2, 3)
- ii) (5, - 3)
- iii) (4, 2)
- iv) (- 7, - 6)
- v) (0, 8)
- vi) (3, 0)
- vii) (-4,0)
- viii) (0, – 6)
- Solution:
- i) (- 2, 3) - Q
_{2}(second quadrant) - ii) (5, - 3) - Q
_{4}(fourth quadrant) - iii) (4, 2) - Q
_{1}(Iirst quadrant) - iv) (- 7, - 6) - Q
_{3}(third quadrant) - v) (0, 8) - on Y-axis
- vi) (3, 0) - on X-axis
- vii) (-4,0) - on X’ - axis
- viii) (0, - 6) - on Y’: axis

Write the abscissae and ordinates of the following points.

- i)(4,-8)
- ii)(-5,3)
- iii)(0,0)
- iv)(5, 0)
- v)(0, -8)

Note: Plural of abscissa is abscissae.

Solution:

Point | abscissa | ordinate |

i) (4, - 8) | 4 | -8 |

ii) (-5, 3) | -5 | 3 |

iii) (0,0) | 0 | 0 |

iv) (5,0) | 5 | 0 |

v) (0,-8) . | 0 | -8 |

Which of the following points lie on the axes ? Also name the axis.

- i) (-5,-8)
- ii) (0, 13)
- iii) (4, - 2)
- iv) (- 2,0)
- v) (0, - 8)
- vi) (7,0)
- vii) (0,0)

Solution:

The points (ii) (0,13) ; (v) (0,- 8) lie on Y - axis.

The points (iv) (- 2, 0), (vi) (7, 0) lie on X - axis.

The point (vii) (0, 0) lie on both X - axis and Y - axis.

The points (i) (- 5, - 8); (iii) (4, – 2) do not lie on any axis.

Write the following based on the graph.

- i) The ordinate of L
- ii) The ordinate of Q
- iii) The point denoted by (- 2,-2)
- iv) The point denoted by (5, – 4)
- v) The abscissa of N
- vi) The abscissa of M

Solution:

- i) - 7
- ii) 7
- iii) The point ’R’
- iv) The point P
- v) 4
- vi) - 3

State true or false and write correct statement.

- i) In the Cartesian plane the horizon-tal line is called Y - axis, if) in the Cartesian plane, the vertical line is called Y – axis.
- iii) The point which lies on both the axes is called origin.
- iv) The point (2, - 3) lies in the third quadrant.
- v) (-5, -8) lies in the fourth quadrant.
- vi) The point (- x, - y) lies in the first quadrant where x < 0; y < 0.

Solution:

i) False

Correct statement: In the Cartesian plane the horizontal line is called X – axis.

ii) True

iii) True

iv) False

Correct statement: The point (2, -3) lies in the fourth quadrant.

v) False

Correct statement: (- 5, - 8) lies in the third quadrant.

vi) True

Plot the following ordered pairs on a graph sheet. What do you observe ?

i) (1, 0), (3, 0), (- 2, 0), (- 5, 0), (0, 0), (5, 0), (- 6, 0)

ii) (0, 1), (0, 3), (0, – 2), (0, – 5), (0, 0), (0,5), (0,-6)

Solution:

i) All points lie on X - axis,

ii) All points lie on Y - axis.

Plot the following points on the Cartesian plane whose x, y co-ordinates are given.

Solution

Are the positions of (5, -8) and (-8, 5) Is same ? JustIfy your answer.

Solution:

The positions of (5, -8) and (-8, 5) are not same. They are two distinct points. (5, -8) lies at a distance of 5 units from Y – axis and 8 units from X – axis on down side of the origin. So it lies in Q_{4}. Where as (- 8, 5) lies in Q_{2}. The point is at a distance of 8 units from Y – axis on left side of the origin and 5 units from X – axis.

What can you say about the position of the points (1, 2), (1, 3), (1, – 4), (1, 0) and (1, 8), Locate on a graph sheet.

Solution:

All the given points lie on a line parallel to Y-axis at a distance of 1 cm.

What can you say about the position of the points (5, 4), (8, 4), (3, 4), (0, 4), (-4, 4), (-2,4)? Locate the points on a graph sheet and justify your answer.

Solution:

The points (5, 4), (8, 4), (3, 4), (0, 4), (- 4, 4) and (- 2, 4) all lie on a line parallel to X-axis at a distance of 4-units from it.

Plot the points (0, 3), (4, 3), (3, 4) (4, 0) in graph sheet. Join the points with straight lines to make a rectangle. Find the area of the rectangle.

Solution:

From the graph, area of the rectangle =12 square units (OR)

Length = 4 units ; breadth = 3 units

A = l/b = 4 × 3 = 12 sq. units.

Plot the points (2, 3), (6, 3) and (4, 7) in a graph sheet. Join them to make it a triangle. Find the area of the triangle.

Solution:

From the graph

Base of the triangle = 4 units

Height of the triangle = 4 units

∴ Area of the triangle = 1/2 × base × height = 1/2 × 4 × 4 = 8sq. units.

Plot at least six points in a graph sheet, each having the sum of its co-ordinates equal to 5. [Hint: (- 2, 7), (1, 4)………….]

Solution:

Given that (x co-ordinate) + (y co-ordinate) = 5

Let the points be

Look at the graph. Write the co-ordinates of the points

A, B, C, D, E, F. G. H, 1, J, K, L, M, N, O, P and Q.

Solution:

A(- 3, 4) ; B(0, 5) : C (3, 4) ; D (2, 4) ; E (2, 0) ;

F (3, 0) ; G (3, - 1) ; H (0, - 1) ; I (- 3, - 1) ;

J (- 3, 0) ; K (- 2, 0) ; L (- 2, 4) ; M (- 1, 0) ;

N (-1, 3); O (0, 0) ; P (1. 3) and Q (1, 0)

In a graph sheet plot each pair of points, join them by line segments.

- i) (2, 5), (4, 7)
- ii) (-3, 5) (-1,7)
- iii) (-3, -4), (2, -4)
- iv) (-3, -5) (2, -5)
- v) (4, -2), (4, -3)
- vi) (-2, 4), (-2, 3)
- vii) (-2, 1), (-2, 0)

Now join the following pairs of points by straight line segments, in the same graph.

- viii) (-3, 5), (-3, 4)
- ix) (2, 5), (2, -4)
- x) (2, -4), (4, -2)
- xi) (2, -4), (4, -3)
- xii) (4, -2), (4, 7)
- xiii) (4, 7), (-1, 7)
- xiv) (-3, 2), (2, 2)

Now you will get a surprise figure. What is it ?

Solution:

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