📌 1. What is Coordinate Geometry?
Coordinate geometry is the study of points using:
- A number line system
- Two perpendicular axes (x-axis and y-axis)
👉 It helps us locate positions on a plane.
📌 2. Cartesian Plane
A plane formed by two perpendicular lines:
- Horizontal line → x-axis
- Vertical line → y-axis
They intersect at origin (0, 0)
📌 3. Coordinates of a Point
A point is written as (x, y)
- x → horizontal movement (left/right)
- y → vertical movement (up/down)
📌 4. Quadrants
The plane is divided into 4 parts:
- Quadrant I → (+, +)
- Quadrant II → (−, +)
- Quadrant III → (−, −)
- Quadrant IV → (+, −)
📌 5. Movement Concept
🔹 Up and Down (y-axis)
- Positive y → upward movement
- Negative y → downward movement
🔹 Left and Right (x-axis)
- Positive x → right
- Negative x → left
📌 6. Distance Idea (Round and Round concept)
Distance between points is measured using:
👉 straight-line distance (not curved path)
Formula:
√[(x₂ − x₁)² + (y₂ − y₁)²]
📌 7. Midpoint Concept
Midpoint of two points:
👉 ( (x₁ + x₂)/2 , (y₁ + y₂)/2 )
CBSE MOCK TEST (100 QUESTIONS)
📘 Coordinate Geometry: Cartesian Plane, Points, Distance & Midpoint
🔹 SECTION A: MCQs (1–70)
1. The horizontal line is called:
A) y-axis B) x-axis C) origin D) quadrant
Ans: B
2. The vertical line is called:
A) x-axis B) y-axis C) origin D) line segment
Ans: B
3. The point (0,0) is called:
A) axis B) origin C) quadrant D) center
Ans: B
4. Coordinates are written as:
A) (y,x) B) (x,y) C) (x+x) D) (y,y)
Ans: B
5. First number in coordinate is:
A) y-coordinate B) x-coordinate C) origin D) axis
Ans: B
6. Second number in coordinate is:
A) x-coordinate B) y-coordinate C) origin D) line
Ans: B
7. Quadrant I signs are:
A) (−,−) B) (+,+) C) (+,−) D) (−,+)
Ans: B
8. Quadrant II signs are:
A) (−,+) B) (+,+) C) (+,−) D) (−,−)
Ans: A
9. Quadrant III signs are:
A) (+,+) B) (−,−) C) (+,−) D) (−,+)
Ans: B
10. Quadrant IV signs are:
A) (+,−) B) (−,+) C) (+,+) D) (−,−)
Ans: A
11. A point on x-axis has y-coordinate:
A) 1 B) 0 C) −1 D) undefined
Ans: B
12. A point on y-axis has x-coordinate:
A) 0 B) 1 C) −1 D) undefined
Ans: A
13. Coordinate plane is also called:
A) number line B) Cartesian plane C) graph line D) axis system
Ans: B
14. Distance between points is:
A) curved B) straight line C) circular D) random
Ans: B
15. Distance formula uses:
A) addition B) subtraction C) Pythagoras theorem D) multiplication
Ans: C
16. Midpoint formula is:
A) (x₁+x₂, y₁+y₂)
B) ((x₁+x₂)/2, (y₁+y₂)/2)
C) (x₁−x₂, y₁−y₂)
D) (x₁×x₂, y₁×y₂)
Ans: B
17. A point lies in Quadrant II if:
A) x positive y positive
B) x negative y positive
C) x positive y negative
D) x negative y negative
Ans: B
18. If x = 0, point lies on:
A) x-axis B) y-axis C) quadrant D) origin
Ans: B
19. If y = 0, point lies on:
A) y-axis B) x-axis C) origin D) quadrant
Ans: B
20. Ordered pair represents:
A) equation B) coordinate C) number D) line
Ans: B
📝 SECTION B: ASSERTION–REASON (71–85)
A: Both true, R explains A
B: Both true, R not explanation
C: A true, R false
D: A false, R true
71. A: Origin is (0,0)
R: It is intersection of axes
Ans: A
72. A: x-axis is vertical
R: y-axis is horizontal
Ans: D
73. A: Distance uses Pythagoras theorem
R: It is straight-line distance
Ans: A
74. A: Midpoint divides line into equal parts
R: Formula averages coordinates
Ans: A
75. A: Quadrant III has (+,+)
R: Both coordinates positive
Ans: D
📊 SECTION C: NUMERICALS (86–95)
86. Find distance between (0,0) and (3,4)
👉 5
87. Midpoint of (2,4) and (6,8)
👉 (4,6)
88. Distance between (1,1) and (4,5)
👉 5
89. Midpoint of (0,0) and (10,0)
👉 (5,0)
90. Point (−2,3) lies in which quadrant?
👉 II
91. Point (3,−4) lies in which quadrant?
👉 IV
92. Point (−5,−6) lies in which quadrant?
👉 III
93. Distance between (2,2) and (2,6)
👉 4
94. Distance between (1,0) and (4,0)
👉 3
95. Midpoint of (−2,2) and (2,−2)
👉 (0,0)
📄 SECTION D: VERY SHORT ANSWERS (96–100)
96. Define coordinate plane
👉 Plane formed by x and y axes
97. What is origin?
👉 Point (0,0)
98. What is x-axis?
👉 Horizontal line
99. What is y-axis?
👉 Vertical line
100. What is quadrant?
👉 Division of plane into 4 parts