Class 10 Math Coordinate Geometry MCQ Test

Class 10 Math Coordinate Geometry MCQ Test: Strengthen your skills with free online multiple-choice questions for CBSE Class 10 Math Chapter 7. Master the concepts of coordinate geometry, including distance, section formula, and applications. Ideal for CBSE exam preparation and competitive tests.

Coordinate Geometry MCQ Test Quiz

Time: 10 Minutes for 10 Question.

10th Math: Coordinate Geometry

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About Coordinate Geometry MCQ Test

Chapter 7 of the CBSE Class 10 Math curriculum, titled “Coordinate Geometry,” introduces fundamental concepts related to the coordinate plane, including distance between points, section formula, and the equation of a line. This chapter is crucial for understanding how geometric shapes can be represented and analyzed using coordinates. The free MCQ quiz provided in this chapter will help students reinforce their understanding and prepare effectively for their CBSE examinations.

Key Concepts Covered:

Coordinate Plane:
- Definition: A two-dimensional plane defined by two perpendicular axes, the x-axis (horizontal) and the y-axis (vertical), intersecting at the origin (0,0).
- Coordinates: Each point on the plane is represented by an ordered pair
  
  $(x, y)$ , where
  
  $x$ is the distance from the y-axis and
  
  $y$ is the distance from the x-axis.
Distance Formula:
- Definition: The distance
  
  $d$ between two points $x_1, y_1)$
  
  $(x_{1}, y_{1})$ and $x_2, y_2)$
  
  $(x_{2}, y_{2})$ is given by: $\sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}$
  
  $d = (x^{2} - x^{1})^{2} + (y^{2} - y^{1})^{2}$
- Application: Used to find the distance between any two points on the coordinate plane.
Midpoint Formula:
- Definition: The midpoint $x_m, y_m)$
  
  $(x_{m}, y_{m})$ of a line segment connecting two points $x_1, y_1)$
  
  $(x_{1}, y_{1})$ and $x_2, y_2)$
  
  $(x_{2}, y_{2})$ is given by: $(xm,ym)=(x1+x22,y1+y22)\left( x_m, y_m \right) = \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$
  
  $(x_{m}, y_{m}) = (2 x ^{1} + x ^{2}, 2 y ^{1} + y ^{2})$
- Application: Used to find the center point of a line segment.
Section Formula:
- Definition: The coordinates of a point dividing a line segment joining $x_1, y_1)$
  
  $(x_{1}, y_{1})$ and $x_2, y_2)$
  
  $(x_{2}, y_{2})$ in the ratio
  
  $m : n$ are given by: $(mx2+nx1m+n,my2+ny1m+n)\left( \frac{mx_2 + nx_1}{m + n}, \frac{my_2 + ny_1}{m + n} \right)$
  
  $(m + n m x ^{2} + n x ^{1}, m + n m y ^{2} + n y ^{1})$
- Application: Useful for finding the coordinates of a point that divides a segment into a given ratio.
Equation of a Line:
- Slope-Intercept Form: The equation of a line can be expressed as:
  
  $y = m x + c$ where
  
  $m$ is the slope of the line and
  
  $c$ is the y-intercept.
- Point-Slope Form: If a line passes through $x_1, y_1)$
  
  $(x_{1}, y_{1})$ with slope
  
  $m$ , its equation is: $y – y_1 = m(x – x_1)$
  
  $y - y_{1} = m (x - x_{1})$
- Two-Point Form: The equation of a line through two points $x_1, y_1)$
  
  $(x_{1}, y_{1})$ and $x_2, y_2)$
  
  $(x_{2}, y_{2})$ is: $y−y1y2−y1=x−x1x2−x1\frac{y – y_1}{y_2 – y_1} = \frac{x – x_1}{x_2 – x_1}$
  
  $y ^{2} - y ^{1} y - y ^{1} = x ^{2} - x ^{1} x - x ^{1}$
Distance of a Point from a Line:
- Definition: The perpendicular distance
  
  $d$ from a point $x_0, y_0)$
  
  $(x_{0}, y_{0})$ to the line
  
  $A x + B y + C = 0$ is given by: $\frac{|Ax_0 + By_0 + C|}{\sqrt{A^2 + B^2}}$
  
  $d = A ^{2} + B ^{2} ∣ A x ^{0} + B y ^{0} + C ∣$
- Application: Used to find the shortest distance from a point to a line.
Applications in Coordinate Geometry:
- Real-Life Problems: Solve problems involving geometric shapes and their properties using coordinates. Examples include finding distances, midpoints, and equations of lines in practical contexts.

Quiz Structure:

The MCQ quiz for this chapter includes a series of questions designed to test students’ understanding of coordinate geometry concepts, including distance, midpoint, section formula, and equations of lines. These questions cover definitions, formulas, and applications of coordinate geometry. The interactive format allows students to practice and assess their knowledge effectively.

Conclusion:

Practicing with the Class 10 Math Coordinate Geometry MCQ Test Chapter 7 is an excellent way for CBSE students to prepare for their exams. This chapter provides a thorough understanding of coordinate geometry, including how to work with distances, midpoints, and equations of lines. The MCQ quiz helps reinforce these concepts, ensuring students are well-prepared for their academic assessments and competitive exams.

Sanjay Kumar

Math educator (6-12) with an MSc from Delhi University and quiz content creator at QuizRanker.org.