Coordinate Geometry Case Study Questions Class 10

Coordinate Geometry Case Study Questions Class 10

Quadratic Equations Case Study Class 10

Coordinate Geometry Case Study Questions Class 10

Understanding Coordinate Geometry Case Study Questions Class 10 is essential for students preparing for board exams. These Case Study Questions Class 10 allow learners to apply the concepts of distance formula, section formula, and area of triangles in real-life contexts. Since Class 10 is a milestone year, solving Math Case Study Class 10 helps students strengthen concepts and build exam confidence.

Importance of Case Study Questions Class 10

Practicing Case Study Class 10 enhances logical thinking and analytical skills. Students learn to connect geometry formulas with real-world problems like navigation, architecture, and city planning. Teachers recommend Case Study Questions Class 10 for thorough revision as they highlight both strengths and weak areas. By solving such case studies, learners develop deeper understanding and problem-solving ability.

Preparation with Online Tests

Our free online practice tests on Case Study Questions Class 10 include step-by-step solutions and explanations. These Math Case Study Questions Class 10 cover a wide variety of problem situations to ensure effective learning. Regular practice with Case Study Class 10 questions boosts accuracy, confidence, and performance in CBSE exams.

Case Study 1: Geometry Logo Design

Case Study 1: Geometry Logo Design

Rohan, a student of class 10, is designing a logo for his school’s annual science exhibition. The logo is a geometrical pattern created on a coordinate plane. He has fixed the three main vertices of the logo at points $A(2, 3)$, $B(6, 1)$, and $C(4, 5)$. The logo’s design is based on the properties of the triangle formed by these three points. He wants to know the shape of the triangle, its area, and the properties of the line segments within it to perfect his design. Rohan’s friend, who is good at programming, also wants to find the coordinates of a point that divides one of the sides of this triangle in a specific ratio. This logo will be displayed on a banner, and for that, he needs to find out the coordinates of the point that is equidistant from all three vertices, as this point will be the center of a circular design element.

1. What is the distance between vertices $A$ and $B$?

  • A) $\sqrt{20}$ units
  • B) $\sqrt{26}$ units
  • C) $2\sqrt{5}$ units
  • D) $4\sqrt{2}$ units
Answer: A) $\sqrt{20}$ units
Solution: Using the distance formula for $A(2, 3)$ and $B(6, 1)$: \[ d = \sqrt{(6 – 2)^2 + (1 – 3)^2} = \sqrt{16 + 4} = \sqrt{20} \, \text{units.} \]

2. Find the area of the triangle $ABC$.

  • A) 4 sq. units
  • B) 6 sq. units
  • C) 8 sq. units
  • D) 10 sq. units
Answer: B) 6 sq. units
Solution: Using the formula: \[ \text{Area} = \tfrac{1}{2}\left| 2(1-5) + 6(5-3) + 4(3-1) \right| = \tfrac{1}{2} |-8 + 12 + 8| = \tfrac{1}{2}(12) = 6 \, \text{sq. units.} \]

3. What are the coordinates of the midpoint of line segment $AC$?

  • A) $(3, 4)$
  • B) $(3, 5)$
  • C) $(4, 4)$
  • D) $(3, 3)$
Answer: A) $(3, 4)$
Solution: Midpoint of $A(2, 3)$ and $C(4, 5)$: \[ x = \tfrac{2+4}{2} = 3, \quad y = \tfrac{3+5}{2} = 4 \] Hence midpoint is $(3, 4)$.

4. Find the coordinates of a point $P$ that divides line segment $BC$ in ratio $2:1$ internally.

  • A) $\left(\tfrac{16}{3}, \tfrac{7}{3}\right)$
  • B) $\left(\tfrac{14}{3}, \tfrac{7}{3}\right)$
  • C) $\left(\tfrac{14}{3}, \tfrac{13}{3}\right)$
  • D) $\left(\tfrac{14}{3}, \tfrac{11}{3}\right)$
Answer: D) $\left(\tfrac{14}{3}, \tfrac{11}{3}\right)$
Solution: Using section formula for $B(6,1)$ and $C(4,5)$: \[ x = \tfrac{2(4) + 1(6)}{3} = \tfrac{14}{3}, \quad y = \tfrac{2(5) + 1(1)}{3} = \tfrac{11}{3} \] So $P = \left(\tfrac{14}{3}, \tfrac{11}{3}\right)$.

5. If Rohan wants to place a circular element at the point equidistant from all three vertices $A,B,C$, what are the coordinates of the center?

  • A) $(4, 3)$
  • B) $(4, 4)$
  • C) $(5, 3)$
  • D) $(5, 4)$
Answer: None of the above (Correct coordinates: $\left(\tfrac{13}{3}, \tfrac{8}{3}\right)$)
Solution: The circumcenter $(x,y)$ satisfies $PA=PB=PC$. Solving the equations gives: \[ (x, y) = \left(\tfrac{13}{3}, \tfrac{8}{3}\right). \]

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