Math Case Study Coordinate Geometry Class 9

Math Case Study Coordinate Geometry Class 9

coordinate geometry case study questions class 9 | Free Online Test

Math Case Study Coordinate Geometry Class 9

Students preparing for exams often search for Case Study math questions for class 9. These exercises help strengthen concepts in the coordinate geometry. Our online tests include interactive math case study questions class 9 that focus on real-life applications of numbers. Practicing these questions regularly improves accuracy and speed. Additionally, students develop problem-solving skills while applying formulas in practical situations.

Importance of Math Case Study Coordinate Geometry Class 9

Math case study questions class 9 encourage analytical thinking and logical reasoning. For instance, questions on rational and irrational numbers allow deeper understanding. Furthermore, solving these problems enhances critical thinking. Short exercises help reinforce key formulas. Therefore, students gain confidence and clarity in the coordinate geometry through consistent practice.

Benefits of Online Test Practice

Our math case study questions online tests provide instant feedback and performance tracking. Students can identify errors quickly and improve their approach. The coordinate geometry case study questions class 9 cover various difficulty levels. Consequently, learners strengthen concepts efficiently and are better prepared for exams. Regular practice ensures mastery of fundamental coordinate geometry topics.

Case Study 1: Coordinate Geometry

In a city map, the Cartesian plane is used to represent various important landmarks. The origin $(0,0)$ is chosen as the City Center. The $x$-axis represents the East-West road, and the $y$-axis represents the North-South road. A school is located at $(4,3)$, a hospital at $(-5,2)$, and a railway station at $(-3,-4)$. A park is located at $(6,-2)$. Students are tasked to analyze these positions using the concepts of coordinate geometry. They must recall that the distance between two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by \[ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}. \] They should also remember that the midpoint of a line joining two points $(x_1,y_1)$ and $(x_2,y_2)$ is \[ M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right), \] and the slope of a line joining $(x_1,y_1)$ and $(x_2,y_2)$ is \[ m=\frac{y_2-y_1}{x_2-x_1}. \] Using these basic results of coordinate geometry, answer the following questions:

MCQ Questions

1. The distance between the School $(4,3)$ and the Hospital $(-5,2)$ is:

  • A) $9$
  • B) $\sqrt{82}$
  • C) $5$
  • D) $\sqrt{90}$
Answer: B) $\sqrt{82}$
Solution: \[ d=\sqrt{(4-(-5))^2+(3-2)^2}=\sqrt{9^2+1^2}=\sqrt{82}. \]

2. The midpoint of the line joining the Hospital $(-5,2)$ and Railway Station $(-3,-4)$ is:

  • A) $(-4,-1)$
  • B) $(-2,-1)$
  • C) $(-4,1)$
  • D) $(-3,0)$
Answer: A) $(-4,-1)$
Solution: \[ M=\left(\frac{-5+(-3)}{2}, \frac{2+(-4)}{2}\right)=\left(\frac{-8}{2}, \frac{-2}{2}\right)=(-4,-1). \]

3. The slope of the line joining the School $(4,3)$ and the Park $(6,-2)$ is:

  • A) $-\tfrac{5}{2}$
  • B) $\tfrac{5}{2}$
  • C) $2$
  • D) $-\tfrac{2}{5}$
Answer: A) $-\tfrac{5}{2}$
Solution: \[ m=\frac{-2-3}{6-4}=\frac{-5}{2}=-\tfrac{5}{2}. \]

4. The coordinates of the point which divides the line joining the School $(4,3)$ and the Park $(6,-2)$ in the ratio $2:3$ internally are:

  • A) $(4.8,1)$
  • B) $(5,-1)$
  • C) $(5.2,0.8)$
  • D) $(6,1)$
Answer: A) $(4.8,1)$
Solution: Using the section formula: \[ \left(\frac{2 \cdot 6+3 \cdot 4}{2+3}, \frac{2 \cdot (-2)+3 \cdot 3}{2+3}\right)=\left(\frac{12+12}{5}, \frac{-4+9}{5}\right)=(\tfrac{24}{5},1)=(4.8,1). \]

5. Which quadrant is the Hospital $(-5,2)$ located in?

  • A) First Quadrant
  • B) Second Quadrant
  • C) Third Quadrant
  • D) Fourth Quadrant
Answer: B) Second Quadrant
Solution: Since $x<0$ and $y>0$, the point lies in the second quadrant.

Your Results:

Correct Answers: 0

Incorrect Answers: 0

Percentage Score: 0%

Educational Resources Footer

Free Educational Resources

Free Study Material English Vocabulary Tests Grammar for Hearing Impaired Math for Hearing Impaired English Vocabulary Case Study Questions Math GRE Vocabulary Tests LaTeX Tutorial R Programming Tests Online English Games Online Math Games Learn Computer Basics JEE Math Tests CAT Quant Tests Increase Calculation Speed Class 10 Math Tests Prompt Engineering SAT Math Tutorial Logic Quizzes Grade 1 Logic Quizzes Grade 2

© 2023 Udgam Welfare Foundation. All rights reserved.