Question Bank — Orienting Yourself: The Use of Coordinates

Section A — MCQs (10 questions, 1 mark each)

1. The coordinates of the origin in the Cartesian plane are
(a) (x, 0) (b) (0, y) (c) (0, 0) (d) (1, 1)

2. A point P(x, y) lies in Quadrant III. The signs of x and y are
(a) (+, +) (b) (−, +) (c) (−, −) (d) (+, −)

3. The point (−3, 0) lies on
(a) the x-axis (b) the y-axis (c) Quadrant II (d) Quadrant IV

4. If a point lies on the y-axis, its coordinates are of the form
(a) (x, 0) (b) (0, y) (c) (x, y) (d) (0, 0)

5. The distance between points (x₁, y₁) and (x₂, y₂) is given by
(a) |x₂ − x₁| (b) |y₂ − y₁| (c) √[(x₂ − x₁)² + (y₂ − y₁)²] (d) (x₂ − x₁) + (y₂ − y₁)

6. Point Q(−5, 3) lies in which quadrant?
(a) I (b) II (c) III (d) IV

7. In the coordinate system, distances to the right of the origin are
(a) negative (b) positive (c) zero (d) undefined

8. The x-coordinate of a point is its perpendicular distance from the
(a) x-axis (b) y-axis (c) origin (d) both axes

9. Assertion-Reason

Assertion (A): The point (4.5, 0) lies on the x-axis.
Reason (R): Any point of the form (x, 0) lies on the x-axis.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

10. Assertion-Reason

Assertion (A): The distance between (3, 4) and (7, 1) is 5 units.
Reason (R): Distance is found using the Baudhāyana–Pythagoras theorem: √[(7−3)² + (1−4)²].
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.

Section B — Very Short Answer (6 questions, 2 marks each)

1. State the coordinates of a point that lies on the positive y-axis at a distance of 4 units from the origin.
2. In which quadrant does the point (−2.9, 0) lie? Give reason.
3. What are the signs of the coordinates of a point lying in Quadrant IV?
4. Write the general form of coordinates of any point on the x-axis.
5. If a point has x-coordinate = 0 and y-coordinate = −4.5, where does it lie?
6. Name the axes that intersect at the origin.

Section C — Short Answer (5 questions, 3 marks each)

1. Find the distance between points A(3, 4) and D(7, 1) using the Baudhāyana–Pythagoras theorem.
2. A point P lies on the x-axis and is 4.5 units to the right of the origin. Write its coordinates and state the quadrant (if any).
3. The points B₁(0, 1.5) and B₂(0, 4) represent the ends of a door. Find the length of this door.
4. State the coordinates of the fourth corner of a rectangle whose three corners are at (8, 9), (11, 9) and (11, 7).
5. Find the distance between (0, 0) and (0, −4.5).

Section D — Long Answer (3 questions, 5 marks each)

1. Derive the formula for the distance between two points (x₁, y₁) and (x₂, y₂) in the Cartesian plane using the Baudhāyana–Pythagoras theorem. Show all steps with a labelled diagram. (Multi-step derivation)
2. In Reiaan’s room (Fig. 1.3), D₁R₁ is the door with R₁(11.5, 0). If the door is 1 unit wide, find the coordinates of D₁. Also calculate the distance of D₁ from the y-axis.
3. Plot the points R(3, 0), A(0, −2), M(−5, −2) and P(−5, 2). Join them in order. Identify (i) two sides perpendicular to each other, (ii) one side parallel to an axis, and (iii) two points that are mirror images across an axis. Justify each answer.

Section E — Case/Source-Based (2 questions, 4 marks each)

Case 1: City Grid Layout

A city has two main roads crossing at the centre (origin) running North–South and East–West. All other streets are 200 m apart and parallel to these roads. Street intersections are named (n, m) where n is the N–S street number and m is the E–W street number.

(i) If the origin is the intersection of the central N–S and E–W roads, what are the coordinates of the intersection of the 4th N–S street and the 3rd E–W street?
(ii) How many street intersections can be referred to as (4, 3)?
(iii) Using the scale 1 cm = 200 m, what is the actual distance between intersections (2, 5) and (4, 5)?
(iv) In which quadrant would the intersection (3, −2) lie if negative numbers were allowed?

Case 2: Reiaan’s Study Table

Reiaan’s rectangular study table has three feet at (8, 9), (11, 9) and (11, 7) on a coordinate grid (1 cm = 1 foot).

(i) Find the coordinates of the fourth foot.
(ii) Calculate the length and width of the table.
(iii) Is this table parallel to the coordinate axes? Justify.
(iv) Find the distance between the feet at (8, 9) and (11, 7).