NCERT/ CBSE Class 9 Maths Chapter 1/ Orienting Yourself The Use of Coordinates/ Extra Questions and MCQ with Answers for Exam Preparation
Coordinate Geometry / Orienting Yourself: The Use of Coordinates
Interactive NCERT/CBSE-style practice worksheet for exam preparation.
NCERT / CBSE Maths Class 9 Chapter 1, Interactive Quiz, MCQs, True/False, Fill in the Blanks and Match the FollowingPart A — Multiple Choice Questions (MCQs)
Q1. Which ancient Indian city was traditionally used as an important reference meridian in Indian astronomical calculations?
The Greek mathematician Ptolemy referred to this location as “Ozine”.
Answer: C. Ujjayin─л
Ujjayin─л was an important reference meridian in ancient Indian astronomical traditions.
Ujjayin─л was an important reference meridian in ancient Indian astronomical traditions.
Q2. Whose mathematical work included a systematic treatment of zero and positive and negative numbers?
This mathematician made important contributions to the arithmetic of zero and negative numbers.
Answer: D. Brahmagupta
Brahmagupta gave an important systematic treatment of zero and positive and negative numbers.
Brahmagupta gave an important systematic treatment of zero and positive and negative numbers.
Q3. If a point P lies in Quadrant III of the Cartesian plane, what must be true about its coordinates (x,y)?
Consider the directions relative to the origin for both the horizontal and vertical axes.
Answer: C. x < 0 and y < 0
Quadrant III is the region where both coordinates are negative.
Quadrant III is the region where both coordinates are negative.
Q4. According to the general definition of coordinates in 2-D space, what does the x-coordinate of a point P(x,y) represent?
Think about which axis determines the horizontal position.
Answer: B. The perpendicular distance from the y-axis
The x-coordinate gives the horizontal position of a point relative to the y-axis.
The x-coordinate gives the horizontal position of a point relative to the y-axis.
Q5. Using the Baudh─Бyana-Pythagoras Theorem, calculate the distance between point A(3,4) and point D(7,1).
Calculate the horizontal and vertical shifts first, then square them and find their sum.
Answer: C. 5 units
√[(7−3)² + (1−4)²]
= √[4² + (−3)²]
= √(16 + 9)
= √25 = 5 units
√[(7−3)² + (1−4)²]
= √[4² + (−3)²]
= √(16 + 9)
= √25 = 5 units
Q6. Which mathematician made important early use of geometric methods for solving algebraic equations, including cubic equations?
This Persian mathematician made important contributions to algebra and geometric solutions of cubic equations.
Answer: D. ├Цmar Khayy─Бm
Omar Khayyam used geometric constructions to study and solve cubic equations.
Omar Khayyam used geometric constructions to study and solve cubic equations.
Q7. A rectangular table has three feet placed at (8,9), (11,9), and (11,7). Where is the fourth foot located?
Consider the vertical and horizontal lines formed by the existing points.
Answer: B. (8,7)
The fourth vertex shares the x-coordinate of the first point and the y-coordinate of the third point.
The fourth vertex shares the x-coordinate of the first point and the y-coordinate of the third point.
Q8. When point A(3,4) is reflected across the y-axis to become point A′, what are the coordinates of A′?
A reflection across the y-axis changes the sign of x, but not y.
Answer: A. (−3,4)
Reflection in the y-axis changes (x,y) to (−x,y).
Reflection in the y-axis changes (x,y) to (−x,y).
Q9. What is the distance between points P(x₁,y₁) and Q(x₂,y₂) that lie on a line parallel to the x-axis?
The vertical change is zero because both points have the same y-coordinate.
Answer: C. |x₂−x₁|
Since y₁ = y₂, only the horizontal difference contributes to the distance.
Since y₁ = y₂, only the horizontal difference contributes to the distance.
Q10. If point Q(y,x) coincides with point P(x,y), what must be true about the relationship between x and y?
Think about when two ordered pairs are equal.
Answer: C. x = y
(y,x) = (x,y) only when both corresponding components are equal.
(y,x) = (x,y) only when both corresponding components are equal.
Q11. If the door in a room is represented by D₁ at (8,0) and R₁ at (11.5,0), what is the width of the door?
Measure the segment between the two points on the x-axis.
Answer: A. 3.5 feet
11.5 − 8 = 3.5 feet.
11.5 − 8 = 3.5 feet.
Q12. Which quadrant would contain the point Q(−5,3)?
Check the signs of the x- and y-coordinates.
Answer: A. Quadrant II
Negative x and positive y means Quadrant II.
Negative x and positive y means Quadrant II.
Q13. A rectangular grid is fixed with pins and threads on the floor of a room. Various key points of the room were marked using pins. Points representing corners of objects were connected with thick wool so that their positions could be felt with fingers. Scale: 1 cm : 1 foot. According to the source, why is the position of windows unable to be marked on the map provided in this figure?
Think about the height of a window relative to the floor shown in the sketch.
Answer: B. The map only shows the 2-D floor layout.
The height of a window requires a third dimension, whereas the floor plan represents two dimensions.
The height of a window requires a third dimension, whereas the floor plan represents two dimensions.
Q14. In the history of navigation, what was the astrolabe designed to help observers determine?
The device linked observations of celestial bodies with geographic position.
Answer: A. Geographic position using observations of celestial bodies
Astrolabes were astronomical instruments used for observations that could help determine latitude and other positional information.
Astrolabes were astronomical instruments used for observations that could help determine latitude and other positional information.
Q15. If a point G is on the y-axis and located 4.5 units downward from the origin, what are its coordinates?
A point on the y-axis has x = 0. Downward means a negative y-value.
Answer: B. (0,−4.5)
Q16. Which civilisation is noted for planned cities with grid-like street layouts and streets running in carefully organised directions?
Think of the ancient South Asian civilisation known for carefully planned urban settlements.
Answer: A. Sindhu-Sarasvat─л Civilisation
Several Indus/Sindhu-Sarasvat─л urban settlements show carefully planned streets and city layouts.
Several Indus/Sindhu-Sarasvat─л urban settlements show carefully planned streets and city layouts.
Q17. If the bathroom door is defined by points A(0,1.5) and B(0,4), and the room door width is 3.5 feet, which door is wider?
Bathroom door width = 4 − 1.5 = 2.5 feet.
Answer: D. The room door is wider
Bathroom door = 2.5 feet; room door = 3.5 feet.
Bathroom door = 2.5 feet; room door = 3.5 feet.
Q18. What mathematical contribution by ─Аryabhaс╣нa made astronomical trigonometric calculations more convenient compared with earlier Greek chord-based methods?
The innovation involved a change in the trigonometric function used for astronomical calculations.
Answer: D. Using sines instead of the Greek chord-based approach
─Аryabhaс╣нa's sine-based trigonometric tables were an important development in astronomical mathematics.
─Аryabhaс╣нa's sine-based trigonometric tables were an important development in astronomical mathematics.
Q19. Point S has coordinates (3,−5). In which quadrant does it lie?
Identify the signs of the horizontal and vertical coordinates.
Answer: A. Quadrant IV
Positive x and negative y means Quadrant IV.
Positive x and negative y means Quadrant IV.
Q20. In a coordinate system, what is the origin and what are its standard coordinates?
Consider the mathematical zero point where the two axes meet.
Answer: D. The point of intersection of the axes; (0,0)
Q21. If a point P lies on the x-axis and is located to the left of the origin, what can be concluded about its coordinates?
Points on the x-axis have y = 0; left of the origin means x is negative.
Answer: B. Its x-coordinate is negative and its y-coordinate is zero
Q22. The Arabic geographical name “Arin” refers to which central longitude reference point associated with early astronomical geography?
The location was associated with an ancient Indian astronomical meridian.
Answer: A. Ujjayin─л
Q23. What is the distance between point A(3,0) and point B(7,0)?
Calculate the difference between the two x-coordinates.
Answer: C. 4 feet
|7 − 3| = 4.
|7 − 3| = 4.
Q24. Which mathematician's 1637 CE work is strongly associated with the formal development of the Cartesian coordinate framework?
The “Cartesian” plane is named after this mathematician.
Answer: D. Ren├й Descartes
Descartes is traditionally associated with the development and formalisation of the Cartesian coordinate framework.
Descartes is traditionally associated with the development and formalisation of the Cartesian coordinate framework.
Q25. In a bathroom, if the corners are O(0,0), F(0,10), R(−6,10), and P(−6,0), what is the length of the wall represented by segment FR?
The two points have the same y-coordinate, so compare their x-coordinates.
Answer: A. 6 units
|0 − (−6)| = 6 units.
|0 − (−6)| = 6 units.
Q26. If a triangle ╬ФADM is reflected in the x-axis, which statement about its properties is true?
Think about whether a mirror reflection changes the size or side lengths of a figure.
Answer: C. The lengths of its sides remain the same
Reflection preserves lengths and angles.
Reflection preserves lengths and angles.
Q27. A circle K is centered at the origin O(0,0). If point A(1,−8) lies on the circle, what is the radius of circle K?
The radius is the distance from the centre to any point on the circle.
Answer: D. √65
OA = √[(1−0)² + (−8−0)²]
= √(1 + 64)
= √65
OA = √[(1−0)² + (−8−0)²]
= √(1 + 64)
= √65
Q28. What happens to the coordinates of a point (x,y) when it is reflected in the origin?
Reflection through the origin reverses the direction along both axes.
Answer: D. It becomes (−x,−y)
Reflection in the origin changes both coordinate signs.
Reflection in the origin changes both coordinate signs.
Part B — True / False
Q29. A point in Quadrant III has both x-coordinate and y-coordinate negative.
Recall the signs of coordinates in Quadrant III.
Answer: True.
Quadrant III contains points for which x < 0 and y < 0.
Quadrant III contains points for which x < 0 and y < 0.
Q30. Every point on the y-axis has a positive x-coordinate.
What is the x-coordinate of every point on the y-axis?
Answer: False.
Every point on the y-axis has x = 0.
Every point on the y-axis has x = 0.
Q31. Reflection in the y-axis changes (x,y) into (−x,y).
Only the horizontal direction changes in reflection across the y-axis.
Answer: True.
Q32. The origin has coordinates (1,1).
The origin is where both axes intersect.
Answer: False.
The origin is (0,0).
The origin is (0,0).
Q33. The distance between (3,0) and (7,0) is 4 units.
Both points lie on the x-axis.
Answer: True.
|7 − 3| = 4.
|7 − 3| = 4.
Part C — Fill in the Blanks
Q34. The point where the x-axis and y-axis intersect is called the ________.
Its coordinates are (0,0).
Answer: Origin
Q35. Every point on the x-axis has its ________ equal to zero.
Think about the second coordinate of (x,0).
Answer: y-coordinate
Q36. A point to the left of the origin on the x-axis has a ________ x-coordinate.
Left of zero on the number line means less than zero.
Answer: Negative
Q37. The Cartesian plane is divided into ________ quadrants.
I, II, III and IV.
Answer: Four (4)
Q38. The distance from O(0,0) to A(1,−8) is ________.
Use √(1² + 8²).
Answer: √65
Part D — Match the Following
Q39. Match Column A with the correct option in Column B.
1. Origin
2. Point (−5,3)
3. Reflection in y-axis
4. Radius for O(0,0), A(1,−8)
5. Quadrant III
Origin = (0,0); (−5,3) = Quadrant II; y-axis reflection changes x; radius = √65; Quadrant III has both coordinates negative.
Answer Key:
1 → (0,0)
2 → Quadrant II
3 → x-coordinate changes sign
4 → √65
5 → Both coordinates negative
1 → (0,0)
2 → Quadrant II
3 → x-coordinate changes sign
4 → √65
5 → Both coordinates negative
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