Case Study 1: Cartesian Plane Basics
Ravi’s teacher drew two perpendicular lines intersecting at O. The horizontal line is called x-axis and the vertical line is y-axis. Together, they form the Cartesian plane.
Questions:
- Point O is called:
(a) origin (b) axis (c) vertex (d) midpoint
Answer: (a) - Coordinates of origin are:
(a) (1,1) (b) (0,0) (c) (1,0) (d) (0,1)
Answer: (b) - The horizontal axis is:
(a) y-axis (b) x-axis (c) z-axis (d) none
Answer: (b) - The vertical axis is:
(a) x-axis (b) y-axis (c) diagonal (d) none
Answer: (b) - The plane is divided into:
(a) 2 parts (b) 3 parts (c) 4 quadrants (d) 8 quadrants
Answer: (c)
Case Study 2: Quadrants
Points A(2,3), B(−4,5), C(−2,−6), D(3,−5) were plotted.
Questions:
- Point A lies in:
(a) I quadrant (b) II (c) III (d) IV
Answer: (a) - Point B lies in:
(a) I (b) II (c) III (d) IV
Answer: (b) - Point C lies in:
(a) I (b) II (c) III (d) IV
Answer: (c) - Point D lies in:
(a) I (b) II (c) III (d) IV
Answer: (d) - Which point has both coordinates negative?
(a) A (b) B (c) C (d) D
Answer: (c)
Case Study 3: On Axes
Teacher gave points P(0,5), Q(−3,0), R(0,0).
Questions:
- P(0,5) lies on:
(a) x-axis (b) y-axis (c) origin (d) none
Answer: (b) - Q(−3,0) lies on:
(a) x-axis (b) y-axis (c) both (d) none
Answer: (a) - R(0,0) is:
(a) x-axis (b) y-axis (c) origin (d) none
Answer: (c) - Any point with x=0 lies on:
(a) x-axis (b) y-axis (c) both (d) none
Answer: (b) - Any point with y=0 lies on:
(a) x-axis (b) y-axis (c) both (d) none
Answer: (a)
Case Study 4: Identifying Coordinates
A cricket ground is mapped on a coordinate plane. The pavilion is at (5,0), the scoreboard at (0,−4).
Questions:
- Pavilion lies on:
(a) x-axis (b) y-axis (c) origin (d) none
Answer: (a) - Scoreboard lies on:
(a) x-axis (b) y-axis (c) origin (d) none
Answer: (b) - Distance of pavilion from origin?
(a) 5 units (b) 4 units (c) 9 units (d) none
Answer: (a) - Distance of scoreboard from origin?
(a) 5 (b) 4 (c) 9 (d) none
Answer: (b) - Which lies below x-axis?
(a) Pavilion (b) Scoreboard (c) Both (d) None
Answer: (b)
Case Study 5: Symmetry of Points
Plot P(2,3) and Q(−2,3).
Questions:
- Points P and Q are symmetric about:
(a) x-axis (b) y-axis (c) origin (d) none
Answer: (b) - Coordinates of reflection of (a,b) in y-axis are:
(a) (a,−b) (b) (−a,b) (c) (−a,−b) (d) none
Answer: (b) - Reflection of (3,−5) in x-axis is:
(a) (3,−5) (b) (−3,−5) (c) (3,5) (d) (−3,5)
Answer: (c) - Reflection of (4,−7) in origin is:
(a) (−4,7) (b) (4,7) (c) (−4,−7) (d) none
Answer: (c) - Reflection of (0,5) in x-axis is:
(a) (0,−5) (b) (0,5) (c) (5,0) (d) (−5,0)
Answer: (a)
Case Study 6: Distance of a Point from Axes
Point A(−7,4).
Questions:
- Distance from y-axis = |x| = ?
(a) 7 (b) 4 (c) 11 (d) none
Answer: (a) - Distance from x-axis = |y| = ?
(a) 7 (b) 4 (c) 11 (d) none
Answer: (b) - Which quadrant does A lie in?
(a) I (b) II (c) III (d) IV
Answer: (b) - A(−7,4) symmetric about y-axis is:
(a) (7,4) (b) (−7,−4) (c) (7,−4) (d) none
Answer: (a) - A(−7,4) symmetric about x-axis is:
(a) (7,4) (b) (−7,−4) (c) (7,−4) (d) none
Answer: (b)
Case Study 7: Plotting Vertices of a Square
Square ABCD has vertices A(0,0), B(0,2), C(2,2), D(2,0).
Questions:
- Length of AB = ?
(a) 2 (b) 0 (c) 4 (d) none
Answer: (a) - Which side lies on y-axis?
(a) AB (b) BC (c) CD (d) DA
Answer: (a) - Which side lies on x-axis?
(a) AB (b) BC (c) CD (d) DA
Answer: (c) - Coordinates of diagonal AC = ?
(a) (0,0),(2,2) (b) (0,2),(2,0) (c) (0,2),(2,2) (d) none
Answer: (a) - Which is true?
(a) ABCD is square (b) rectangle only (c) rhombus only (d) none
Answer: (a)
Case Study 8: Identifying Points
Teacher gave points: P(2,0), Q(0,−3), R(−4,0), S(0,5).
Questions:
- P lies on:
(a) x-axis (b) y-axis (c) origin (d) none
Answer: (a) - Q lies on:
(a) x-axis (b) y-axis (c) none (d) both
Answer: (b) - R lies on:
(a) x-axis (b) y-axis (c) none (d) both
Answer: (a) - S lies on:
(a) x-axis (b) y-axis (c) origin (d) none
Answer: (b) - Which two are on y-axis?
(a) P,Q (b) Q,S (c) R,S (d) none
Answer: (b)
Case Study 9: Geometry Application
Triangle vertices are A(0,0), B(4,0), C(0,3).
Questions:
- Which axis does AB lie on?
(a) x-axis (b) y-axis (c) both (d) none
Answer: (a) - Which axis does AC lie on?
(a) x-axis (b) y-axis (c) both (d) none
Answer: (b) - Coordinates of C are:
(a) (3,0) (b) (0,3) (c) (4,0) (d) none
Answer: (b) - Which point is at origin?
(a) A (b) B (c) C (d) none
Answer: (a) - What type of triangle is ABC?
(a) right-angled (b) isosceles (c) scalene (d) equilateral
Answer: (a)
Case Study 10: Map Activity
On a city map, school is at (−2,3), hospital at (3,3), park at (0,−4).
Questions:
- School lies in:
(a) I quadrant (b) II (c) III (d) IV
Answer: (b) - Hospital lies in:
(a) I (b) II (c) III (d) IV
Answer: (a) - Park lies in:
(a) I (b) II (c) III (d) IV
Answer: (d) - Which two lie on same line parallel to x-axis?
(a) school, hospital (b) hospital, park (c) school, park (d) none
Answer: (a) - Which point has negative y-coordinate?
(a) school (b) hospital (c) park (d) none
Answer: (c)