MCQS with Answers on Chapter 1 'Orienting Yourself: The Use of Coordinates' for Class 9

MCQs on Chapter 1: Orienting Yourself – The Use of Coordinates for Class 9 Maths are available in this Maths article along with a free PDF for offline practice. These multiple‑choice questions help students practise the key concepts from Chapter 1 of the CBSE Maths syllabus in an exam‑oriented format. The MCQs with answers and detailed solutions, prepared by our subject experts, cover the Cartesian plane, coordinates of a point, x‑axis and y‑axis, abscissa and ordinate, quadrants and their sign patterns, plotting points, and finding distances between points on the plane to strengthen conceptual understanding and improve problem‑solving skills. By practising MCQs on Chapter 1: Orienting Yourself – The Use of Coordinates, students can improve accuracy, understand formulas better, and build confidence for board exams.

MCQS on Chapter 1: Orienting Yourself - The Use of Coordinates for Class 9 With Answers

Question 1: What are the coordinates of the origin?

(A) (1, 0)

(B) (0, 1)

(C) (1, 1)

(D) (0, 0)

Answer: (D) (0, 0)

Explanation: The origin is the point where the x-axis and y-axis intersect. It is zero units from both axes, so its coordinates are (0, 0).

Question 2: The x-coordinate of a point is also called its:

(A) Ordinate

(B) Abscissa

(C) Intercept

(D) Origin

Answer: (B) Abscissa

Explanation: The x-coordinate represents the perpendicular distance of the point from the y-axis, measured along the x-axis. This is called the abscissa.

Question 3: What is the y-coordinate of every point that lies on the x-axis?

(A) 0

(B) 1

(C) Any positive number

(D) Undefined

Answer: (A) 0

Explanation: Any point on the x-axis lies at zero vertical distance from the x-axis. So all such points have y-coordinate 0 and are written as (x, 0).

Question 4: The point S(3, –5) lies in which quadrant?

(A) Quadrant I

(B) Quadrant II

(C) Quadrant III

(D) Quadrant IV

Answer: (D) Quadrant IV

Explanation: S(3, –5) has x = 3 (positive) and y = –5 (negative). Points with positive x and negative y lie in Quadrant IV. 

Question 5: Both x-coordinate and y-coordinate of a point are negative. The point lies in:

(A) Quadrant I

(B) Quadrant II

(C) Quadrant III

(D) Quadrant IV

Answer: (C) Quadrant III

Explanation: Points in Quadrant III have both x- and y-coordinates negative.

Question 6: The point (0, 7) lies:

(A) In Quadrant I

(B) On the y-axis, above the origin

(C) On the x-axis, to the right of the origin

(D) In Quadrant II

Answer: (B) On the y-axis, above the origin

Explanation: x = 0 means the point is on the y-axis. y = 7 is positive, so the point is above the origin.

Question 7: What is the distance between M(9, 6) and A(3, 4)?

(A) √29 units

(B) √20 units

(C) √40 units

(D) √50 units

Answer: (C) √40 units

Explanation: MA = √[(3–9)² + (4–6)²] = √[(–6)² + (–2)²] = √[36 + 4] = √40 units.

Question 8: The distance between two points on the x-axis, say (x₁, 0) and (x₂, 0), is:

(A) x₂ + x₁

(B) x₂ × x₁

(C) |x₂ – x₁|

(D) √(x₁² + x₂²)

Answer: (C) |x₂ – x₁|

Explanation: The distance between points (x₁, y) and (x₂, y) is the absolute value |x₂ – x₁| of the difference between x₁ and x₂.

Question 9: Is M(3, 4) the midpoint of segment joining S(2, 3) and T(4, 5)?

(A) Yes

(B) No, the midpoint is (3, 4.5)

(C) No, the midpoint is (2, 3)

(D) Yes, because 3 and 4 are averages of 2, 4 and 3, 5

Answer: (D) Yes, because 3 and 4 are averages of 2, 4 and 3, 5

Explanation: Midpoint = ((2+4)/2, (3+5)/2) = (6/2, 8/2) = (3, 4). Since this equals M(3, 4), yes, M is the midpoint.

Question 10: Are the points M(–3, –4), A(0, 0), and G(6, 8) collinear (on the same straight line)?

(A) No, they form a triangle

(B) Yes, they are collinear

(C) Cannot be determined without plotting

(D) Yes, but only if they are in the same quadrant

Answer: (B) Yes, they are collinear

Explanation: MA = √[(0–(–3))² + (0–(–4))²] = √[9 + 16] = 5.

AG = √[(6–0)² + (8–0)²] = √[36 + 64] = 10.

MG = √[(6–(–3))² + (8–(–4))²] = √[81 + 144] = √225 = 15.

Since MA + AG = 5 + 10 = 15 = MG, the three points are collinear. 

Question 11: points A(1, –8), B(–4, 7), and C(–7, –4) lie on a circle centered at origin O(0, 0). What is the radius of this circle?

(A) √55

(B) √65

(C) √75

(D) √85

Answer: (B) √65

Explanation: Radius = OA = √[(1–0)² + (–8–0)²] = √[1 + 64] = √65.

Question 12: A circular icon of radius 80 pixels has its centre at A(100, 150) on a screen 800 pixels wide and 600 pixels high (origin at bottom-left). Does any part of the circle extend outside the screen?

(A) Yes, it extends beyond the top of the screen

(B) Yes, it extends beyond the left side

(C) No, the circle is fully within the screen

(D) Yes, it extends beyond the bottom

Answer: (C) No, the circle is fully within the screen

Explanation: Centre A = (100, 150), radius = 80. Check all four sides:

Left: 100 – 80 = 20 > 0

Right: 100 + 80 = 180 < 800 

Bottom: 150 – 80 = 70 > 0 

Top: 150 + 80 = 230 < 600

All sides are clear, so the circle lies entirely within the screen. 

Question 13: The three feet of Reiaan's rectangular study table are at (8, 9), (11, 9), and (11, 7). Where is the fourth foot?

(A) (8, 7)

(B) (7, 8)

(C) (9, 8)

(D) (8, 11)

Answer: (A) (8, 7)

Explanation: A rectangle has four corners. Three are at (8, 9), (11, 9), and (11, 7). The x-coordinates used are 8 and 11; the y-coordinates are 9 and 7. The missing corner must have x = 8 and y = 7, giving (8, 7).

Question 14: What is the distance between the points (0, 0) and (5, 12)?

(A) 17 units

(B) 13 units

(C) 11 units

(D) 7 units

Answer: (B) 13 units

Explanation: Distance from origin = √[(5–0)² + (12–0)²] = √[25 + 144] = √169 = 13 units.

Question 15: Does the distance formula give a different result if we take (x₂ – x₁) or (x₁ – x₂)?

(A) Yes, the result is different because the sign changes

(B) No, because we square the difference

(C) Yes, the result changes in sign but not in magnitude

(D) Only when x₁ > x₂

Answer: (B) No, because we square the difference

Explanation: It makes no difference whether (x₂ – x₁) and (y₂ – y₁) are positive or negative, as both differences are squared, (x₂–x₁ )² = (x₁–x₂ )².

 

Click here to download the free PDF of MCQs worksheet on Chapter 1: Orienting Yourself - The Use of Coordinates for Class 9 Maths based on the updated NCERT & CBSE pattern with important multiple-choice questions and answers.

MCQs Worksheet on Chapter 1: Orienting Yourself - The Use of Coordinates for Class 9