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CHAPTER 1 — THE USE OF COORDINATES
Class IX Mathematics — Coordinate Geometry
Preeti Kushwah Classes — Unit Test (Set 1: Foundation)
General Instructions:
1. All questions are compulsory.
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Draw neat figures wherever required. Use graph paper for plotting questions.
1. All questions are compulsory.
2. Section A has 6 questions of 1 mark each.
3. Section B has 5 questions of 2 marks each.
4. Section C has 4 questions of 3 marks each.
5. Section D has 2 questions of 5 marks each.
6. Draw neat figures wherever required. Use graph paper for plotting questions.
Section A — (1 Mark Each) [6 × 1 = 6]
Q1.1
The point where the x-axis and y-axis intersect is called ___. Write its coordinates.
Q2.1
The abscissa of the point (−3, 5) is ___.
Q3.1
In which quadrant does the point (−4, −7) lie?
Q4.1
True or False: The point (0, −5) lies in the third quadrant.
Q5.1
A point on the x-axis has coordinates of the form: (a) (x, 0) or (b) (0, y)? Choose the correct option.
Q6.1
Write the coordinates of a point 6 units to the left of the origin on the x-axis.
Section B — (2 Marks Each) [5 × 2 = 10]
Q7.2
Identify the quadrant or axis for each point: (3, −1), (−4, 6), (0, 3), (−2, 0)
Q8.2
Write the abscissa and ordinate of each point: P(7, −3), Q(−5, 2), R(0, −8), S(4, 0)
Q9.2
A point has abscissa −3 and ordinate 5. Write its coordinates and name the quadrant it lies in.
Q10.2
Fill in the blanks:
(a) The x-coordinate of every point on the y-axis is ___.
(b) The coordinate axes divide the plane into ___ parts called ___.
(c) The perpendicular distance of point (5, 7) from the y-axis is ___.
(d) Point (−4, 0) lies on the ___ axis.
(a) The x-coordinate of every point on the y-axis is ___.
(b) The coordinate axes divide the plane into ___ parts called ___.
(c) The perpendicular distance of point (5, 7) from the y-axis is ___.
(d) Point (−4, 0) lies on the ___ axis.
Q11.2
A point lies on the y-axis at a distance of 4 units below the origin. Write its coordinates.
Section C — (3 Marks Each) [4 × 3 = 12]
Q12.3
Plot A(1, 1), B(1, 4), C(4, 4), D(4, 1). Join ABCD in order.
(a) Name the figure formed.
(b) Find the length of each side.
(c) Find the perimeter.
(a) Name the figure formed.
(b) Find the length of each side.
(c) Find the perimeter.
Q13.3
From the following points, identify which lie in: (i) Quadrant II (ii) on the x-axis (iii) on the y-axis
Points: (3, 0), (−2, 5), (0, −7), (−1, −3), (0, 4), (6, −2), (−5, 0), (4, 7)
Points: (3, 0), (−2, 5), (0, −7), (−1, −3), (0, 4), (6, −2), (−5, 0), (4, 7)
Q14.3
Three vertices of a rectangle are A(2, 1), B(2, 4), C(6, 4). Find the fourth vertex D and plot the rectangle.
Q15.3
Write two points in each of the four quadrants and two points on each axis (total 12 points).
Section D — (5 Marks Each) [2 × 5 = 10]
Q16.5
A teacher draws a seating plan on a Cartesian plane. Desks are placed at:
Row 1: (1,1), (2,1), (3,1), (4,1)
Row 2: (1,2), (2,2), (3,2), (4,2)
Row 3: (1,3), (2,3), (3,3), (4,3)
(a) Plot all 12 desks on the Cartesian plane. [1]
(b) Aman sits at (3, 2). Write the coordinates of his neighbours (left, right, front, back). [1]
(c) Priya moves from (1, 1) to (4, 3). How many units right and up does she move? [1]
(d) The teacher stands at the origin. Which desk is closest to the teacher? [1]
(e) If the room is expanded by adding column x = 5 and row y = 4, how many new desks are added? List their coordinates. [1]
Row 1: (1,1), (2,1), (3,1), (4,1)
Row 2: (1,2), (2,2), (3,2), (4,2)
Row 3: (1,3), (2,3), (3,3), (4,3)
(a) Plot all 12 desks on the Cartesian plane. [1]
(b) Aman sits at (3, 2). Write the coordinates of his neighbours (left, right, front, back). [1]
(c) Priya moves from (1, 1) to (4, 3). How many units right and up does she move? [1]
(d) The teacher stands at the origin. Which desk is closest to the teacher? [1]
(e) If the room is expanded by adding column x = 5 and row y = 4, how many new desks are added? List their coordinates. [1]
Q17.5
Plot the points A(−4, 3), B(3, 3), C(3, −2), D(−4, −2). Join ABCD.
(a) What shape is formed? [1]
(b) Find the lengths AB and BC. [1]
(c) Find the perimeter and area. [1]
(d) Which sides are parallel to the axes? [1]
(e) Write the coordinates where the sides cross the x-axis and the y-axis. [1]
(a) What shape is formed? [1]
(b) Find the lengths AB and BC. [1]
(c) Find the perimeter and area. [1]
(d) Which sides are parallel to the axes? [1]
(e) Write the coordinates where the sides cross the x-axis and the y-axis. [1]
Bonus Question (Optional) [2 Marks]
Q18.2
★ A point P lies in the second quadrant. Its distance from the x-axis is 5 units and from the y-axis is 3 units. Find the coordinates of P. If P is reflected in the x-axis, what are the new coordinates and which quadrant will it lie in?
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Answer Key & Detailed Solutions
Q1. [1 Mark]
Origin. Coordinates: (0, 0).
Q2. [1 Mark]
−3. (The abscissa is the x-coordinate.)
Q3. [1 Mark]
Quadrant III. (Both coordinates are negative → Quadrant III.)
Q4. [1 Mark]
False. The point (0, −5) lies on the y-axis (x-coordinate is 0), not in any quadrant.
Q5. [1 Mark]
(a) (x, 0). Points on the x-axis always have y-coordinate = 0.
Q6. [1 Mark]
(−6, 0). Moving left means negative x-direction.
Q7. [2 Marks]
(3, −1) → Quadrant IV (x positive, y negative)
(−4, 6) → Quadrant II (x negative, y positive)
(0, 3) → y-axis (x = 0)
(−2, 0) → x-axis (y = 0)
[½ mark each]
(−4, 6) → Quadrant II (x negative, y positive)
(0, 3) → y-axis (x = 0)
(−2, 0) → x-axis (y = 0)
[½ mark each]
Q8. [2 Marks]
P(7, −3): abscissa = 7, ordinate = −3
Q(−5, 2): abscissa = −5, ordinate = 2
R(0, −8): abscissa = 0, ordinate = −8
S(4, 0): abscissa = 4, ordinate = 0
[½ mark each]
Q(−5, 2): abscissa = −5, ordinate = 2
R(0, −8): abscissa = 0, ordinate = −8
S(4, 0): abscissa = 4, ordinate = 0
[½ mark each]
Q9. [2 Marks]
Coordinates = (−3, 5). Since x is negative and y is positive, the point lies in Quadrant II.
[1 mark for coordinates, 1 mark for quadrant]
[1 mark for coordinates, 1 mark for quadrant]
Q10. [2 Marks]
(a) 0
(b) 4 parts called quadrants
(c) 5 units
(d) x-axis
[½ mark each]
(b) 4 parts called quadrants
(c) 5 units
(d) x-axis
[½ mark each]
Q11. [2 Marks]
The point is on the y-axis (x = 0) and 4 units below origin (y = −4).
Coordinates: (0, −4).
[1 mark for reasoning, 1 mark for answer]
Coordinates: (0, −4).
[1 mark for reasoning, 1 mark for answer]
Q12. [3 Marks]
(a) Square. [1 mark]
(b) AB = |4−1| = 3, BC = |4−1| = 3, CD = |4−1| = 3, DA = |4−1| = 3.
All sides = 3 units. [1 mark]
(c) Perimeter = 4 × 3 = 12 units. [1 mark]
(b) AB = |4−1| = 3, BC = |4−1| = 3, CD = |4−1| = 3, DA = |4−1| = 3.
All sides = 3 units. [1 mark]
(c) Perimeter = 4 × 3 = 12 units. [1 mark]
Q13. [3 Marks]
(i) Quadrant II (x negative, y positive): (−2, 5) [1 mark]
(ii) On x-axis (y = 0): (3, 0), (−5, 0) [1 mark]
(iii) On y-axis (x = 0): (0, −7), (0, 4) [1 mark]
(ii) On x-axis (y = 0): (3, 0), (−5, 0) [1 mark]
(iii) On y-axis (x = 0): (0, −7), (0, 4) [1 mark]
Q14. [3 Marks]
In rectangle ABCD: A(2,1), B(2,4), C(6,4).
AB is vertical (x = 2), BC is horizontal (y = 4).
D must have x = 6 (same as C) and y = 1 (same as A).
D = (6, 1).
[2 marks for finding D, 1 mark for plot]
AB is vertical (x = 2), BC is horizontal (y = 4).
D must have x = 6 (same as C) and y = 1 (same as A).
D = (6, 1).
[2 marks for finding D, 1 mark for plot]
Q15. [3 Marks]
Sample answer:
QI: (2, 3), (5, 1)
QII: (−3, 4), (−1, 7)
QIII: (−2, −5), (−4, −1)
QIV: (6, −3), (1, −2)
x-axis: (4, 0), (−3, 0)
y-axis: (0, 5), (0, −2)
[½ mark per correct pair in each region]
QI: (2, 3), (5, 1)
QII: (−3, 4), (−1, 7)
QIII: (−2, −5), (−4, −1)
QIV: (6, −3), (1, −2)
x-axis: (4, 0), (−3, 0)
y-axis: (0, 5), (0, −2)
[½ mark per correct pair in each region]
Q16. [5 Marks]
(a) Plot all 12 points on grid. [1 mark]
(b) Left: (2, 2), Right: (4, 2), Front (above): (3, 3), Back (below): (3, 1). [1 mark]
(c) Right: 4 − 1 = 3 units. Up: 3 − 1 = 2 units. [1 mark]
(d) Desk (1, 1) — closest to origin (distance = √(1+1) = √2 ≈ 1.41). [1 mark]
(e) New desks: (5,1), (5,2), (5,3), (5,4), (1,4), (2,4), (3,4), (4,4) = 8 new desks. [1 mark]
(b) Left: (2, 2), Right: (4, 2), Front (above): (3, 3), Back (below): (3, 1). [1 mark]
(c) Right: 4 − 1 = 3 units. Up: 3 − 1 = 2 units. [1 mark]
(d) Desk (1, 1) — closest to origin (distance = √(1+1) = √2 ≈ 1.41). [1 mark]
(e) New desks: (5,1), (5,2), (5,3), (5,4), (1,4), (2,4), (3,4), (4,4) = 8 new desks. [1 mark]
Q17. [5 Marks]
(a) Rectangle. [1 mark]
(b) AB = 3 − (−4) = 7 units. BC = 3 − (−2) = 5 units. [1 mark]
(c) Perimeter = 2(7 + 5) = 24 units. Area = 7 × 5 = 35 sq units. [1 mark]
(d) AB and CD are parallel to x-axis. BC and DA are parallel to y-axis. [1 mark]
(e) DA crosses x-axis at (−4, 0). BC crosses x-axis at (3, 0). AB crosses y-axis at (0, 3). DC crosses y-axis at (0, −2). [1 mark]
(b) AB = 3 − (−4) = 7 units. BC = 3 − (−2) = 5 units. [1 mark]
(c) Perimeter = 2(7 + 5) = 24 units. Area = 7 × 5 = 35 sq units. [1 mark]
(d) AB and CD are parallel to x-axis. BC and DA are parallel to y-axis. [1 mark]
(e) DA crosses x-axis at (−4, 0). BC crosses x-axis at (3, 0). AB crosses y-axis at (0, 3). DC crosses y-axis at (0, −2). [1 mark]
Q18. Bonus [2 Marks]
In Quadrant II: x is negative, y is positive.
Distance from x-axis = |y| = 5, so y = 5.
Distance from y-axis = |x| = 3, so x = −3.
P = (−3, 5). [1 mark]
Reflection in x-axis: (x, y) → (x, −y) = (−3, −5).
This lies in Quadrant III. [1 mark]
Distance from x-axis = |y| = 5, so y = 5.
Distance from y-axis = |x| = 3, so x = −3.
P = (−3, 5). [1 mark]
Reflection in x-axis: (x, y) → (x, −y) = (−3, −5).
This lies in Quadrant III. [1 mark]