Case Study Coordinate Geometry Class 9

Case Study Coordinate Geometry Class 9

Case Study Coordinate Geometry Class 9 | Free Online Test

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 2: Coordinate Geometry

A farmer uses a Cartesian plane to plan his farmland layout. The farmhouse is located at $(2,5)$, a water well at $(-4,3)$, the barn at $(0,-6)$, and a warehouse at $(6,-3)$. He wishes to connect these locations with roads in straight lines. To calculate the required road lengths and optimize the layout, he uses concepts from coordinate geometry. Recall that the distance formula between $(x_1,y_1)$ and $(x_2,y_2)$ is \[ d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}, \] the midpoint formula is \[ M=\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right), \] and the slope of a line joining two points is \[ m=\frac{y_2-y_1}{x_2-x_1}. \] Also, two lines are perpendicular if $m_1 \cdot m_2 = -1$, and parallel if $m_1=m_2$.

MCQ Questions

1. The distance between the Farmhouse $(2,5)$ and the Water well $(-4,3)$ is:

  • A) $2\sqrt{10}$
  • B) $\sqrt{40}$
  • C) $\sqrt{45}$
  • D) $3\sqrt{5}$
Answer: A) $2\sqrt{10}$
Solution: \[ d=\sqrt{(2-(-4))^2+(5-3)^2}=\sqrt{6^2+2^2}=\sqrt{40}=2\sqrt{10}. \]

2. The midpoint of the line joining the Barn $(0,-6)$ and Warehouse $(6,-3)$ is:

  • A) $(3,-4.5)$
  • B) $(3,-3)$
  • C) $(2,-4.5)$
  • D) $(2,-3)$
Answer: A) $(3,-4.5)$
Solution: \[ M=\left(\frac{0+6}{2}, \frac{-6+(-3)}{2}\right)=(3,-4.5). \]

3. The slope of the line joining the Farmhouse $(2,5)$ and the Barn $(0,-6)$ is:

  • A) $\tfrac{11}{2}$
  • B) $-\tfrac{11}{2}$
  • C) $\tfrac{2}{11}$
  • D) $-\tfrac{2}{11}$
Answer: A) $\tfrac{11}{2}$
Solution: \[ m=\frac{-6-5}{0-2}=\frac{-11}{-2}=\tfrac{11}{2}. \]

4. Which of the following lines is perpendicular to the line joining Farmhouse $(2,5)$ and Barn $(0,-6)$?

  • A) A line with slope $\tfrac{11}{2}$
  • B) A line with slope $-\tfrac{2}{11}$
  • C) A line with slope $\tfrac{2}{11}$
  • D) A line with slope $-\tfrac{11}{2}$
Answer: B) A line with slope $-\tfrac{2}{11}$
Solution: If $m_1 \cdot m_2=-1$, then slope of required line is \[ m_2=-\frac{1}{\tfrac{11}{2}}=-\tfrac{2}{11}. \]

5. In which quadrant does the Warehouse $(6,-3)$ lie?

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

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