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Class 9 Maths: Orienting Yourself, The Use of Coordinates, 8 practice questions with answers

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These are 8 practice questions on Chapter 1, Orienting Yourself: The Use of Coordinates, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part I (First Edition, April 2026). Each has a worked answer and the textbook page it comes from. They cover naming the quadrant of a point, points on the axes, how far a point is from each axis, writing a point from its distances, the distance between two points on a line parallel to an axis, the sides and perimeter of a rectangle on the grid, and the distance formula. Try each one on paper before you open the answer.

These questions are our own, drafted with AI help. Every number was re-computed by a test script and none of the numbers is taken from the chapter, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari, Grade 9, Part I, Chapter 1, printed pages 1 to 15):

Points and quadrants

Question 1. In which quadrant does each point lie: P (−23, 37), Q (−41, −19), R (53, −28), S (26, 44)?

Answer: P in Quadrant II, Q in Quadrant III, R in Quadrant IV, S in Quadrant I. P has a negative x-coordinate and a positive y-coordinate (−, +); Q has both negative (−, −); R has a positive x and a negative y (+, −); S has both positive (+, +). (Quadrants, page 6.)

Question 2. Where do the points T (0, −47) and U (38, 0) lie, and how far is each from the origin?

Answer: T is on the y-axis, 47 units below O; U is on the x-axis, 38 units to the right of O. A point with x-coordinate 0 lies on the y-axis, and its negative y-coordinate puts it below O. A point with y-coordinate 0 lies on the x-axis, and its positive x-coordinate puts it to the right of O. (Points on the axes, pages 3 and 4.)

Question 3. How far is the point K (−36, 25) from the x-axis, and how far from the y-axis? In which quadrant is it?

Answer: 25 units from the x-axis, 36 units from the y-axis; Quadrant II. The y-coordinate gives the perpendicular distance from the x-axis, here 25 units (upwards). The x-coordinate gives the perpendicular distance from the y-axis, here 36 units (to the left, because it is negative). With (−, +) signs the point is in Quadrant II. (Meaning of the coordinates and quadrants, page 6.)

Question 4. A point lies in Quadrant III. It is 39 units from the y-axis and 54 units from the x-axis. Write its coordinates.

Answer: (−39, −54). The distance from the y-axis is the size of the x-coordinate, 39, and the distance from the x-axis is the size of the y-coordinate, 54. In Quadrant III both coordinates are negative, so the point is (−39, −54). (Meaning of the coordinates and quadrants, page 6.)

Distances

Question 5. Find the distance between A (−27, 31) and B (46, 31), and between C (24, −19) and D (24, 58).

Answer: AB = 73 units; CD = 77 units. A and B have the same y-coordinate, so AB is parallel to the x-axis: AB = |46 − (−27)| = 73. C and D have the same x-coordinate, so CD is parallel to the y-axis: CD = |58 − (−19)| = 77. (Distance along a line parallel to an axis, page 15.)

Question 6. A rectangle has corners W (−38, −24), X (57, −24), Y (57, 46) and Z (−38, 46). Find the lengths of its sides and its perimeter. In which quadrant is each corner?

Answer: sides 95 and 70 units; perimeter 330 units; W in III, X in IV, Y in I, Z in II. WX is parallel to the x-axis: |57 − (−38)| = 95. XY is parallel to the y-axis: |46 − (−24)| = 70. Perimeter = 95 + 70 + 95 + 70 = 330 units. The signs of the corners are W (−, −), X (+, −), Y (+, +), Z (−, +). (Distances parallel to the axes, page 15; quadrants, page 6.)

Question 7. Find the distance between E (−59, −19) and F (−35, 26).

Answer: 51 units. Shift along the x-axis: −35 − (−59) = 24. Shift along the y-axis: 26 − (−19) = 45. EF = √(24² + 45²) = √(576 + 2025) = √2601 = 51 units. (Distance formula, page 10.)

Question 8. Find the distance between G (63, −17) and H (27, 60). Does it matter if you subtract the coordinates in the other order?

Answer: 85 units; no, the order does not matter. x₂ − x₁ = 27 − 63 = −36 and y₂ − y₁ = 60 − (−17) = 77. GH = √((−36)² + 77²) = √(1296 + 5929) = √7225 = 85 units. Subtracting the other way gives 36 and −77, whose squares are the same, so the distance is the same: only the size of each shift matters. (Distance formula, page 10; signs of the differences, page 11.)

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Sources

All opened and read on 22 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 0.

The rules and the formula are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.