1. Points A(1, 1) and B(5, 1) are plotted on the grid. How long is AB?
- A5 units
- B4 units
- C2 units
- D6 units
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Answer: B) 4 units
A and B have the same y-coordinate, so AB is horizontal. AB = 5 − 1 = 4 units. (6 comes from adding 5 + 1.)
Class 9 Figures on the Coordinate Plane — practice questions with answers
Coordinate Geometry · 5 sample questions from the school syllabus. Try each one, then open the answer and the worked solution.
2. Look at triangle ABC on the grid with A(1, 1), B(7, 1) and C(4, 5). Find its area.
- A10 sq units
- B12 sq units
- C15 sq units
- D24 sq units
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Answer: B) 12 sq units
Base AB = 7 − 1 = 6 (horizontal). Height = distance of C above AB = 5 − 1 = 4. Area = ½ × 6 × 4 = 12 sq units.
3. The segment joining (−4, 3) and (5, 3) crosses one of the axes. At which point?
- A(0, 3)
- B(1, 3)
- C(0, −4)
- D(3, 0)
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Answer: A) (0, 3)
The segment is horizontal at height y = 3 and runs from x = −4 to x = 5, so it passes x = 0. It meets the y-axis at (0, 3). It never reaches the x-axis because y stays 3.
4. An L-shaped plot has corners (0, 0), (6, 0), (6, 2), (2, 2), (2, 5) and (0, 5). Find its perimeter.
- A20 units
- B22 units
- C24 units
- D18 units
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Answer: B) 22 units
Sides in order: 6, 2, 4, 3, 2, 5. Sum = 22 units. (18 is the area: 6 × 2 + 2 × 3.)
5. A rectangle has two adjacent vertices at (−1, 2) and (5, 2), and its area is 30 sq units. Which could be its other two vertices?
- A(5, 7) and (−1, −3)
- B(5, −3) and (−1, −3)
- C(5, 5) and (−1, 5)
- D(5, 32) and (−1, 32)
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Answer: B) (5, −3) and (−1, −3)
Side along y = 2 has length 5 − (−1) = 6, so the other side is 30 ÷ 6 = 5. The rectangle goes 5 up (y = 7) or 5 down (y = −3); only (5, −3), (−1, −3) is offered as a matching pair. (5, 5) gives height 3, area 18; mixing 7 and −3 does not make a rectangle.
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