HOTS Questions on Chapter 1 ‘Orienting Yourself - The Use of Coordinates’ for Class 9 with Answers

Higher-Order Thinking Skills questions on Chapter 1: Orienting Yourself - The Use of Coordinates for Class 9 are crafted to deepen conceptual understanding and sharpen problem-solving through challenging, real-world scenarios. Aligned with CBSE and NCERT aims, this set moves beyond routine exercises to ask students to analyse, reason, and apply coordinate-geometry ideas like plotting and reading points, calculating distances and midpoints, interpreting slopes, and solving simple locus problems so learners develop flexible mathematical thinking rather than rote procedures.Download the PDF to access the HOTS questions in a printable format, making offline learning and exam revision easier.

Solved HOTS Questions on Coordinate Geometry

Question 1: What is the abscissa of the origin?

Solution:

The origin has coordinates (0, 0). The abscissa is the x-coordinate, so the abscissa of the origin is 0.

Question 2: What is the sign of the y-coordinate of a point that lies below the x-axis?

Solution:

Any point below the x-axis has a negative y-coordinate. This is because we move downward from the origin along the y-axis, which is the negative direction.

Question 3: What are the coordinates of a point lying on the y-axis at −3 units from the origin?

Solution:

A point on the y-axis always has its x-coordinate = 0. If it is 3 units below the origin (i.e., in the negative direction), its coordinates are (0, −3).

Question 4: Two points are A(−3, 7) and B(−7, 5). Find the value of (Abscissa of A) − (Abscissa of B).

Solution:

Abscissa of A = x-coordinate of A = −3

Abscissa of B = x-coordinate of B = −7

Difference = (−3) − (−7) = −3 + 7 = 4

Question 5: A point is such that its abscissa (which is non-zero) equals its ordinate. In which quadrant(s) can this point lie?

Solution:

If abscissa = ordinate, i.e., x = y (and x ≠ 0), then:

If both x and y are positive ⇒ the point lies in Quadrant I (e.g., (3, 3))

If both x and y are negative ⇒  the point lies in Quadrant III (e.g., (−2, −2))

So the point can lie in Quadrant I or Quadrant III.

Question 6: Can a point lie in more than one quadrant at the same time? Give a reason. What about lying on the axes?

Solution:

No, a point cannot lie in more than one quadrant simultaneously. The four quadrants are mutually exclusive, non-overlapping regions of the Cartesian plane. A point has a unique pair of coordinates (x, y) and can belong to exactly one of the four quadrants or to one of the axes but never two simultaneously.

A point that lies on the x-axis or y-axis does not belong to any quadrant. The axes form the boundaries between quadrants, not part of them.

Question 7: A point P lies in the third quadrant. Its distance from the x-axis is 4 units and its distance from the y-axis is 3 units. What are the coordinates of P? Also write the coordinates of its mirror images with respect to (i) the x-axis, (ii) the y-axis, and (iii) the origin.

Solution:

Since P is in Quadrant III, both coordinates are negative.

Distance from x-axis = |y-coordinate| = 4 ⇒ y = −4

Distance from y-axis = |x-coordinate| = 3 ⇒ x = −3

So P = (−3, −4)

(i) Mirror image with respect to the x-axis:

Reflecting over the x-axis changes the sign of the y-coordinate.

⇒ Mirror image = (−3, 4) [Quadrant II]

(ii) Mirror image with respect to the y-axis:

Reflecting over the y-axis changes the sign of the x-coordinate.

⇒ Mirror image = (3, −4) [Quadrant IV]

(iii) Mirror image with respect to the origin:

Reflecting through the origin changes the sign of both coordinates.

⇒ Mirror image = (3, 4) [Quadrant I]

Question 8: A city has two main roads crossing at the centre of the city. These roads are along the North-South and East-West directions. All the other streets of the city run parallel to these two roads and are 200 m apart. There are five streets in each direction. Using the Cartesian system, set up a coordinate system to represent this city. Name the main roads as the x and y-axes, and plot the intersection of the 2nd street (East) and 3rd street (North).

Solution:

Let's set up our coordinate system:

The intersection of the two main roads = Origin (0, 0)

East direction = positive x-axis; West = negative x-axis

North direction = positive y-axis; South = negative y-axis

Each unit = 200 m

Streets are numbered by their distance from the main roads:

1st street East = x = 1, 2nd street East = x = 2, etc.

1st street North = y = 1, 2nd street North = y = 2, etc.

The intersection of the 2nd street East and 3rd street North = (2, 3)

This is a Quadrant I point (both coordinates positive), 400 m East and 600 m North of the city centre.

Question 9: State whether the following are True or False, and explain why:

(a) The point (−2, 3) and the point (3, −2) represent the same location on the Cartesian plane.

False. In an ordered pair (x, y), the first value is always the x-coordinate and the second is always the y-coordinate. (−2, 3) lies in Quadrant II, while (3, −2) lies in Quadrant IV. They are entirely different points.

(b) A point can lie on both the x-axis and y-axis simultaneously.

True, but only at the Origin. The point (0, 0) lies on both axes. No other point satisfies y = 0 and x = 0 at the same time.

Questions PDF with worked-out examples for Class 9 Chapter 1:Orienting Yourself – The Use of Coordinates, perfect for last-minute CBSE exam revision.

Class 10 Chapter 1: Orienting Yourself – The Use of Coordinates HOTS PDF