Welcome to AssamSchool. This article contains 30 Extra Questions from Coordinate Geometry from Class 9 Mathematics Chapter 3. These Coordinate Geometry Class 9 Extra Questions are helpful to test your understanding and knowledge of the chapter. These additional questions will not only help you to excel in the chapter but also will give you a strong foundation in Mathematics.
We have also provided step-by-step answers to the questions for reference. So, let’s start…
30 Coordinate Geometry Class 9 Extra Questions
Extra Questions for Chapter: Coordinate Geometry
1. What are the coordinates of the origin?
Solution:
The coordinates of the origin are (\(0, 0)\).
2. In Fig. A, point \(P\) lies 5 units to the right of the \(y\)-axis and 3 units below the \(x\)-axis. Write its coordinates.
Solution:
Since \(P\) is 5 units right of the \(y\)-axis, \(x = 5\). It is 3 units below the \(x\)-axis, so \(y = -3\). Coordinates: (\(5, -3)\).
3. In which quadrant does the point (\(-7, 4)\) lie?
Solution:
(\(-7, 4)\) has \(x < 0\) and \(y > 0\). Hence, it lies in Quadrant II.
4. Write the coordinates of a point on the \(x\)-axis at a distance of 8 units from the origin to the left.
Solution:
On the \(x\)-axis, \(y = 0\). Left of the origin means \(x = -8\). Coordinates: (\(-8, 0)\).
5. Find the perpendicular distance of the point (\(3, -4)\) from the \(x\)-axis.
Solution:
Distance from the \(x\)-axis = \(|y| = |-4| = 4\) units.
6. A house is located on Street 4, House 7. Represent this as a coordinate.
Solution:
Assuming streets are along the \(x\)-axis and houses along the \(y\)-axis, coordinates: \((4, 7)\).
7. Plot the points \(A(2, 5)\), \(B(-3, 0)\), and \(C(0, -4)\) on a Cartesian plane and label them.
Solution:
- \(A(2, 5)\): 2 units right on \(x\)-axis, 5 units up on \(y\)-axis.
- \(B(-3, 0)\): 3 units left on \(x\)-axis, on the axis.
- \(C(0, -4)\): 4 units down on \(y\)-axis, on the axis.
8. Is \((5, -2)\) correctly labeled as Quadrant III? Justify.
Solution:
No. Quadrant III requires both coordinates negative. \((5, -2)\) is in Quadrant IV.
9. If a point lies on both axes, what are its coordinates?
Solution:
The only point common to both axes is the origin: \((0, 0)\).
10. A point \(Q\) is 6 units left of the origin and 2 units above the \(x\)-axis. Write its coordinates.
Solution:
Coordinates: \((-6, 2)\).
11. Identify the quadrant for \((-1, -5)\).
Solution:
Both coordinates are negative. Hence, Quadrant III.
12. Which axis does the point \((0, 9)\) lie on?
Solution:
\(y\)-axis (since \(x = 0\)).
13. A point \((a, b)\) is 7 units from the \(y\)-axis and 3 units from the \(x\)-axis. What are \(a\) and \(b\)?
Solution:
Distance from \(y\)-axis = \(|a| = 7 \implies a = \pm7\).
Distance from \(x\)-axis = \(|b| = 3 \implies b = \pm3\).
Possible coordinates: \((7, 3)\), \((7, -3)\), \((-7, 3)\), \((-7, -3)\).
14. In a city grid, a café is at cross-street \((3, 7)\). How far is it from the vertical road if each street is 200 m apart?
Solution:
Distance from vertical road = \(3 \times 200 = 600\) m.
15. Plot \((-5, -5)\) and state its quadrant.
Solution:
Both coordinates are negative. The point lies in Quadrant III.
16. A student writes the coordinates of a point as \((y, x)\). Is this correct? Explain.
Solution:
No. Coordinates are written as \((x, y)\), where \(x\) is the distance from the \(y\)-axis.
17. What is common about all points on the \(x\)-axis?
Solution:
Their \(y\)-coordinate is always 0. Coordinates: (\(x, 0)\).
18. In Fig. C, point \(R\) is at \((-2, 4)\). How far is it from the \(y\)-axis?
Solution:
Distance from \(y\)-axis = \(|x| = |-2| = 2\) units.
19. Which quadrant has positive \(x\) and negative \(y\)?
Solution:
Quadrant IV.
20. Write the coordinates of two points on the \(y\)-axis.
Solution:
Examples: \((0, 1)\), \((0, -5)\).
21. A point \((p, q)\) is 4 units from the \(x\)-axis. What can \(q\) be?
Solution:
\(|q| = 4 \implies q = 4\) or \(q = -4\).
22. A park is 3 blocks east and 2 blocks north of the city center. Represent this as coordinates.
Solution:
Coordinates: (\(3, 2)\).
23. Plot \((0, 0)\), \((0, -3)\), and \((4, 0)\) on a Cartesian plane.
Solution:
- \((0, 0)\): Origin.
- \((0, -3)\): 3 units down on \(y\)-axis.
- \((4, 0)\): 4 units right on \(x\)-axis.
24. Is \(( -2, 0)\) in Quadrant II? Justify.
Solution:
No. Points on the \(x\)-axis \((y = 0)\) do not lie in any quadrant.
25. What are the coordinates if a point is equidistant from both axes in Quadrant I?
Solution:
In Quadrant I, \(x = y\). Example: \((5, 5)\).
26. In Fig. D, point \(S(4, -3)\) is reflected over the \(x\)-axis. What are the new coordinates?
Solution:
Reflection over \(x\)-axis changes \(y\) to \(-y\). New coordinates: \((4, 3)\).
27. A point \((0, 9)\) is in which quadrant?
Solution:
It lies on the \(y\)-axis, not in any quadrant.
28. Write the coordinates of a point 6 units below the origin on the \(y\)-axis.
Solution:
\((0, -6)\).
29. If a point is 10 units from the \(y\)-axis, what is its \(x\)-coordinate?
Solution:
\(|x| = 10 \implies x = 10\) or \(x = -10\).
30. In a theater, seat \((7, 5)\) is in row 7, column 5. Is this coordinate format correct? Explain.
Solution:
No. Typically, rows are \(y\)-axis and columns \(x\)-axis. Correct format: \((5, 7)\).
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The Bottom Line
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You can also check the related MCQs for this chapter here: MCQ on Coordinate Geometry
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Abdur Rohman is an Electrical Engineer from Charaideo, Assam, who wears multiple hats as a part-time teacher, blogger, entrepreneur, and digital marketer. Passionate about education, he founded The Assam School blog to provide free, comprehensive textbook solutions, MCQs (Multiple Choice Questions), and other academic content for students from Class V to XII.