Maharashtra Board Practice Worksheet
Class 10 Maths 2 Chapter 5
Coordinate Geometry Worksheet
Practise Maharashtra Board Class 10 Maths 2 Chapter 5 Coordinate
Geometry with MCQs, plotting points, distance formula, section formula,
slope, equations of lines and board-exam-style questions.
Worksheet objective: Improve accuracy in plotting
coordinates, selecting the correct formula and solving coordinate-geometry
problems with complete step-by-step calculations.
Class 10 Coordinate Geometry Worksheet
This Coordinate Geometry worksheet is designed for Maharashtra State
Board students who want structured practice after studying Chapter 5.
It includes questions based on the coordinate plane, quadrants,
distance between two points, section formula, midpoint, slope and
equations of straight lines.
The worksheet begins with concept-based multiple-choice questions and
gradually moves towards calculations and board-exam-style applications.
Students should substitute coordinates carefully, preserve positive
and negative signs and show each mathematical step on a separate line.
(x,y)
Coordinate Plane
Plot ordered pairs and identify the quadrant, axis and position
of each point.
d
Distance and Section
Calculate distances, midpoints and coordinates of points that
divide line segments.
m
Slope and Lines
Calculate slope and use coordinate relationships to study
straight lines.
Important Coordinate Geometry Formulae
Distance = √[(x₂ − x₁)² + (y₂ − y₁)²]
Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Internal division in ratio m:n =
((mx₂ + nx₁)/(m + n), (my₂ + ny₁)/(m + n))
Slope m = (y₂ − y₁)/(x₂ − x₁)
-
Write every point as an ordered pair in the form (x, y).
-
Move horizontally according to the x-coordinate and vertically
according to the y-coordinate.
-
Keep brackets around coordinate differences before squaring.
-
Maintain the same order of points in the numerator and denominator
while calculating slope.
-
A point on the x-axis has y = 0, while a point on the y-axis has
x = 0.
Types of Questions Included
Multiple-Choice Questions
MCQs test ordered pairs, quadrants, signs of coordinates, distance,
midpoint, section formula and slope.
Plotting Points
Students plot points on the Cartesian plane and identify their
quadrants or positions on the coordinate axes.
Distance Formula Questions
These questions require students to substitute two ordered pairs,
simplify the squared differences and calculate the positive square
root.
Section Formula and Midpoint
Students find the coordinates of a point dividing a line segment
in a given ratio. Midpoint questions are treated as division in
the ratio 1:1.
Slope and Straight Lines
Students calculate slope, compare slopes and use coordinate
relationships to study parallel or collinear points.
Board-Exam-Style Problems
Mixed questions combine graphs, algebra and geometry to develop
complete Maharashtra SSC examination preparation.
How to Solve Coordinate Geometry Questions
- Write the coordinates of all given points clearly.
- Identify the formula required by the question.
- Assign (x₁, y₁) and (x₂, y₂) consistently.
- Substitute negative coordinates inside brackets.
- Simplify every coordinate difference carefully.
- Calculate squares and products one step at a time.
- Simplify the square root or coordinate fractions.
- Write the final answer as a length, slope or ordered pair.
Benefits of Practising This Worksheet
- Improves understanding of the Cartesian coordinate plane.
- Strengthens plotting and graph-reading skills.
- Provides practice with distance and section formulae.
- Improves handling of negative coordinates.
- Develops accuracy in slope calculations.
- Encourages complete step-by-step presentation.
- Supports school tests, prelims and SSC Board preparation.
Common Mistakes Students Should Avoid
- Do not interchange the x-coordinate and y-coordinate.
- Do not ignore the negative sign of a coordinate.
- Do not square only one coordinate difference.
- Do not combine the x-part and y-part of the section formula.
- Do not reverse only one difference while calculating slope.
- Do not write a negative value for distance.
- Do not write coordinates without brackets and a comma.
- Check the quadrant before accepting a plotted point.
Check Your Work with Chapter 5 Solutions
Attempt every worksheet question independently and show complete
working. After completing the worksheet, compare your formula,
substitutions and final answers with the complete Chapter 5 Coordinate
Geometry solutions.
View Chapter 5 Solutions →
Frequently Asked Questions
Select any question to view its answer.
What topics are covered in this worksheet?
It covers plotting points, quadrants, distance, midpoint,
section formula, slope and straight-line applications.
What is an ordered pair?
An ordered pair is written as (x, y), where x gives the
horizontal position and y gives the vertical position.
What is the distance formula?
The distance between (x₁, y₁) and (x₂, y₂) is
√[(x₂ − x₁)² + (y₂ − y₁)²].
How is the midpoint calculated?
Add the two x-coordinates and divide by two. Then add the two
y-coordinates and divide by two.
What is the slope of a horizontal line?
The slope of a horizontal line is zero because the change in
the y-coordinate is zero.
Does the worksheet contain MCQs?
Yes. It includes concept-based MCQs, numerical problems and
mixed board-exam-style questions.
Is this useful for Maharashtra SSC preparation?
Yes. It provides structured practice for school tests, prelims
and the Maharashtra SSC Board examination.
When should I check the Chapter 5 solutions?
Check the solutions only after attempting each question and
showing the complete calculation independently.
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