## AP 9th Class Maths Bits 3rd Lesson Co-Ordinate Geometry

Multiple Choice Questions (MCQs) :

Question 1.

The coordinate system used to plot points on a plane is known as the:

A) Cartesian coordinate system

B) polar coordinate system

C) spherical coordinate system

D) cylindrical coordinate system

Answer:

A) Cartesian coordinate system

Question 2.

The horizontal axis on a Cartesian coordinate system is known as the:

A) ordinate

B) abscissa

C) latitude

D) longitude

Answer:

B) abscissa

Question 3.

The vertical axis on a Cartesian coordinate system is known as the:

A) ordinate

B) abscissa

C) latitude

D) longitude

Answer:

A) ordinate

Question 4.

In. the point (3, 4), which number represents the abscissa?

A) 3

B) 4

C) Both 3 and 4

D) Neither 3 nor 4

Answer:

A) 3

Question 5.

In the point (3, 4), which number represents the ordinate?

A) 3

B) 4

C) Both 3 and 4

D) Neither 3 nor 4

Answer:

B) 4

Question 6.

What is the distance between the points (-2, 3) lies in which quadrant ?

A) 1

B) 2

C) 3

D) 4

Answer:

B) 2

Question 7.

Which of the following is an example of a point on a Cartesian coordinate system?

A) (x, y, z)

B) (x, y)

C) (r, θ)

D) (p, Φ, θ)

Answer:

B) (x, y)

Question 8.

The co-ordinates of origin are

A) (0, 9)

B) (0, 1)

C) (0, 0)

D) none of above

Answer:

C) (0, 0)

Question 9.

The x-coordinate of all points on the y-axis on a Cartesian coordinate system is:

A) y = 0

B) x = 0

C) y = 1

D) x = 1

Answer:

B) x = 0

Question 10.

The y-coordinate of all points on the x-axis on a Cartesian coordinate system is:

A) y = 0

B) x = 0

C) y = 1

D) x = 1

Answer:

A) y = 0

Question 11.

Abscissa of a point is positive in

A) I and II quadrants

B) I and IV quadrants

C) I^{st} quadrant only

D) II^{nd} quadrant only.

Answer:

B) I and IV quadrants

Question 12.

The points (-5, 2) and (2, -5) lie in the

A) same quadrant

B) II and III quadrants respectively.

C) II and IV quadrants respectively.

D) I and IV quadrants respectively

Answer:

C) II and IV quadrants respectively.

Question 13.

If (x + 2, 4) = (5, y – 2), then coordinates (x, y) are

A) (7, 12)

B) (6, 3)

C) (3, 6)

D) (2, 1)

Answer:

C) (3, 6)

Question 14.

Mirror image of the point (9, -8) in y – axis is

A) (-9, -8)

B) (9, 8)

C) (-9, 8)

D) (-8, 9)

Answer:

A) (-9, -8)

Question 15.

The coordinates of the point which lies on y-axis at a distance of 4 units in negative direction of y-axis is

A) (5, 4)

B) (4, 0)

C) (0, -4)

D) (-4, 0)

Answer:

C) (0, -4)

Question 16.

If the points A(2, 0), B(-6, 0) and C(3, a – 3) lie on the x-axis, then the value of a is

A) 0

B) 2

C) 3

D) -6

Answer:

C) 3

Question 17.

Which of the following points lies on the negative side of x-axis?

A) (-4, 0)

B) (3, 2)

C) (0, -4)

D) (5, -7)

Answer:

A) (-4, 0)

Question 18.

The Coordinates of point Q are

A) (3, 3.5)

B) (3.5, 3)

C) (-3, 3.5)

D) (-3, -3.5)

Answer:

D) (-3, -3.5)

Question 19.

The point M lies in the IV quadrant. The coordinates of point M are

A) (a, b)

B) (-a, b)

C) (a, -b)

D) (-a, -b)

Answer:

C) (a, -b)

Question 20.

Write the name of the quadrant in which the point (-3, -5) lies.

A) First quadrant

B) Second quadrant

C) Third quadrant

D) Fourth quadrant

Answer:

C) Third quadrant

Question 21.

The number of parts the coordinates axes divide the plane is

A) Two parts

B) Four parts

C) Six parts

D) Eight parts

Answer:

B) Four parts

Question 22.

Point (0, 4) lies

A) in I^{st} quadrant

B) on x-axis

C) on y-axis

D) in IV quadrant

Answer:

B) on x-axis

Question 23.

The mirror image of the point (-3, -4) in x-axis is

A) (-4, -3)

B) (3, -4)

C) (3, 4)

D) (-3, 4)

Answer:

D) (-3, 4)

Question 24.

In which quadrant does the point (-1, 2) lie?

A) First quadrant

B) Second quadrant

C) Third quadrant w

D) Fourth quadrant

Answer:

B) Second quadrant

Question 25.

Abscissa of a point is negative in

A) I and II quadrants

B) I and IV quadrants

C) II and III quadrants

D) IV quadrant only

Answer:

C) II and III quadrants

Question 26.

Abscissa of all the points on y-axis is

A) 1

B) any number

C) 0

D) -1

Answer:

C) 0

Question 27.

Which is the example of geometrical line?

A) Blackboard

B) Sheet of paper

C) Meeting place of two walls

D) Tips of sharp pencil

Answer:

C) Meeting place of two walls

Question 28.

Rene Descartes was a

A) French Mathematician

B) Indian Mathematician

C) Russian Mathematician

D) British Mathematician

Answer:

A) French Mathematician

Question 29.

Rene Descartes belonged to

A) 15th century

B) 16th century

C) 17th century

D) 18th century

Answer:

C) 17th century

Question 30.

Which of the following is an example of a geometrical line ?

A) Blackboard

B) Sheet of paper

C) Metting place of two walls

D) Tip of the sharp pencil

Answer:

C) Metting place of two walls

Question 31.

If x and y, both are positive, then the point (x, y) lines in

A) I quadrant

B) II quadrant

C) III quadrant

D) IV quadrant

Answer:

A) I quadrant

Question 32.

If x is positive and y is negative, then the point (x, y) lies in

A) III quadrant

B) IV quadrant

C) II quadrant

D) I quadrant

Answer:

B) IV quadrant

Question 33.

The line of intersection of II and III quadrants is

A) x – axis

B) y – axis

C) vertical axis

D) none of these

Answer:

A) x – axis

Question 34.

The line of intersection of III and IV quadrants is

A) y – axis

B) x – axis

C) horizontal axis

D) none of these

Answer:

Question 35.

The line of intersection of IV and I quadrants is

A) x – axis

B) y – axis

C) vertical axis

D) none of these

Answer:

A) x – axis

Question 36.

Where do the II and IV quadrants meet ?

A) at ‘0’

B) in y – axis

C) in x – axis

D) do not intersect

Answer:

A) at ‘0’

Question 37.

Where do the four quadrants meet ?

A) at ‘0’

B) in x – axis

C) in y – axis

D) do not meet

Answer:

A) at ‘0’

Question 38.

In fourth quadrant, x is

A) +ve

B) -ve

C) 0

D) none of these

Answer:

A) +ve

Question 39.

In fourth quadrant, y is

A) -ve

B) +ve

C) 0

D) none of these

Answer:

A) -ve

Question 40.

The points (- 5, 2) and (2, – 5) lie in the

A) same quadrant

B) II and III quadrants respectively

C) II and IV quadrants respectively

D) IV and III quadrants respectively

Answer:

C) II and IV quadrants respectively

Question 41.

Abscissa of a point is positive in

A) I and II quadrants

B) V and IV quadrants

C) I quadrant only .

D) IV quadrant only

Answer:

B) V and IV quadrants

Question 42.

In which quadrant does the poipt (- 1, 2) lie ?

A) I

B) II

C) III

D) IV

Answer:

B) II

Question 43.

In which quadrant does the point (-1,-1) lie?

A) I

B) II

C) III

D) IV

Answer:

C) III

Question 44.

In which quadrant does the point (1,-2) lie?

A) I

B) II

C) III

D) IV

Answer:

D) IV

Question 45.

Point (0, 4) lies :

A) in I quadrant

B) on x – axis

C) on y – axis

D) on IV quadrant

Answer:

C) on y – axis

Question 46.

Abscissa of all the points on y – axis is:

A) 1

B) any number

C) 0

D) -1

Answer:

C) 0

Question 47.

Which of the following points lies on the negative side of x – axis ?

A) (-4, 0)

B) (3, 2)

C) (0, -4)

D)(5, -7)

Answer:

A) (-4, 0)

Question 48.

The coordinates of point Q are

A) (3, 3.5)

B) (3.5, 3)

C) (-3, 3.5)

D) (-3, -3.5)

Answer:

D) (-3, -3.5)

Question 49.

The coordinates of the point which lies on y – axis at a distance of 4 units in negative direction of y – axis is

A) (0, 4)

B) (4, 0)

C) (0, -4)

D) (-4, 0)

Answer:

C) (0, -4)

Question 50.

If a point is on negative side of y-axis at a distance of 3 units from origin then, the coordiantes of the point are

A) (0, 3)

B) (0, -3)

C) (3 ,0)

D) (-3, 0)

Answer:

B) (0, -3)

Question 51.

The point which lies on y – axis at a distance of 6 units in the negative direction of y – axis is

A) (0, 6)

B) (6, 0)

C) (0, -6)

D) (-6,0)

Answer:

C) (0, -6)

Question 52.

If the point A(2, 0), B(-6, 0) and C(3, a – 3) lies on the x – axis, then the value of ‘a’ is

A) 0

B) 2

C) 3

D) -6

Answer:

C) 3

Question 53.

If (x + 2, 4) = (5, y – 2), then the coordinates (x, y) are

A) (7, 12)

B) (6, 3)

C) (3, 6)

D) (2, 1)

Answer:

C) (3, 6)

Question 54.

Mirror image of the point (-1, 2) in y – axis is

A) (1, 2)

B) (1, -2)

C) (2, 1)

D)(2, -1)

Answer:

A) (1, 2)

Question 55.

Mirror image of the po1nt (3, 9) In x – axis is

A) (-3, 9)

B) (9, 3)

C) (3, 9)

D) (3, -9)

Answer:

D) (3, -9)

Question 56.

Write the coordinates of p.

A) (2, 2)

B) (-1, -2)

C) (1, -2)

D) (-1, 2)

Answer:

A) (2, 2)

Question 57.

Write the coordinates of p.

A) (1, -3)

B) (1, 3)

C) (-1, -3)

D) (-1, -3)

Answer:

A) (1, -3)

Question 58.

The distance of the point (1, 0) from ‘0’ is

A) 0

B) 1

C) 2

D) none of these

Answer:

B) 1

Question 59.

The distance of the point (-1, 0) from ‘0’ is

A) 0

B) 1

C) -1

D) none of these

Answer:

B) 1

Question 60.

The distance of the point (0, -1) from ‘0’ is

A) 1

B) 0

C) -1

D) none of these

Answer:

A) 1

Question 61.

By plotting the points 0(0, 0), A(1, 0), B(1, 1), C(0, 1) and joining OA, AB, BC and CO, the figure we obtain is

A) square

B) rectangle

C) trapezium

D) rhombus

Answer:

A) square

Question 62.

Match the following.

i) (3, -3) | a) Q1 |

ii) (-2, -2) | b) Q2 |

iii) (1, 1 ) | c) Q3 |

iv) (-5, 5) | d) Q4 |

A) i – d, ii – c, iii – b, iv – a

B) i – b, ii – a, iii – d, iv – c

C) i- d, ii – c, iii – a, iv – b

D) i – d, ii – b, iii – c, iv – a

Answer:

C) i – d, ii – c, iii – a, iv – b

i) (3, -3) | d) Q4 |

ii) (-2, -2) | c) Q3 |

iii) (1, 1 ) | a) Q1 |

iv) (-5, 5) | b) Q2 |

Assertion and Reason Type Questions :

Question 1.

Assertion : The x-axis of a Cartesian plane is also known as the horizontal axis.

Reason : The x-axis represents the values of the horizontal coordinate or abscissa.

Answer:

Both assertion and reason are correct and, the reason is the correct explanation for

the assertion.

Question 2.

Assertion : The origin of a Cartesian plane is the point where the x-axis and the y-axis intersect.

Reason : The coordinates of the origin is (0, 0).

Answer:

Both assertion arid reason are correct and the reason is the correct explanation for

the assertion.

Question 3.

Assertion : The y-axis of a Cartesian plane is also known as the vertical axis.

Reason : The y-axis represents the values of the vertical coordinate or ordinate.

Answer:

Both assertion and reason are correct and the reason is the correct explanation for the assertion.

Question 4.

Assertion : The distance between two points on the Cartesian plane can be calculated using the formula {(x^{2} – x^{1})^{2} + (y^{2} – y^{1})^{2}}.

Reason : The Pythagorean theorem is used to calculate the lengths of sides of right triangle.

Answer:

Both assertion and reason are correct and the reason is not the correct explanation for the assertion.

Question 5.

Question Assertion : The direction of the x-axis on the Cartesian plane is from left to right.

Reason : The direction of the x-axis is determined by the positive direction of the horizontal coordinate.

Answer:

Both assertion and reason are correct and the reason is the correct explanation for the assertion.

Fill in the blanks :

1. The development of coordinate geometry is often attributed to the French mathematician _________ .

Answer:

Rene Descartes

2. The Cartesian coordinate system is named after Rene Descartes’ Latinized name, _________ .

Answer:

Cartesian

3. The development of coordinate geometry revolutionized mathematics by allowing geometric problems to be solved using _________ .

Answer:

algebraic equations

4. The concept of using coordinates to represent geometric figures was first introduced by the Greek mathematician _________ .

Answer:

Apollonius of Perga

5. The study of algebraic geometry, which combines algebra and geometry using coordinate systems, was further developed in the 19^{th} century by mathematicians such as _________ .

Answer:

Carl Friedrich Gauss and Arthur Cayley

6. The _________ axis is the horizontal line on the Cartesian plane.

Answer:

X-axis

7. The _________ axis is the vertical line on the Cartesian plane.

Answer:

Y-axis

8. The point where the X-axis and Y-axis intersect is called the _________ .

Answer:

origin

9. A point on the Cartesian plane is represented as a pair of numbers in the form of _________ .

Answer:

(x, y)

10. The Cartesian plane is divided into four regions called _________ .

Answer:

quadrants

11. We can plot the point (2, 3) on the Cartesian plane in _________ quadrant.

Answer:

Q_{1}

12. Which quadrant does the point located at (-4, 5) on the Cartesian plane ?

Answer:

Q_{2}

13. Drawn line connecting the points (-3, 2) and (1, 6) goes through the _________ , _________ quadrants on the Cartesian plane.

Answer:

Q_{1} and Q_{2}

14. Which quadrant does the point (-2, -7) lie on the Cartesian plane?

Answer:

Q_{3}

15. Plot the points (0, 4), (2, 1) and (-3, 2) on the Cartesian plane and connect them, we get _________ .

Answer:

a triangle

16. What are the names of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane ? _________

Answer:

Horizontal line – x-axis, Vertical line – y-axis

17. The sum of the abscissa and ordinate of a point of intersection of coordinate axes is _________ .

Answer:

0 [That point is origin (0, 0)]

18. Draw a rough diagram of Cartesian plane.

Answer:

19. The position of (2, 3) and (3, 2) represent same on the graph paper. (True or False) _________ .

Answer:

False