Tuesday, May 17, 2022

# Year 10 Coordinate Geometry Test

## Practice Questions For Class 10 Maths Chapter 7 Coordinate Geometry

Year 10 Test Review: Geometry & Measurement
• The centre of a circle is . Find the values of a, if the circle passes through the point and has a diameter 10 2 units.
• Find the ratio in which the line 2x + 3y 5 = 0 divides the line segment joining the points and . Also, find the coordinates of the point of division.
• Show that the points , , and are the vertices of a square.
• Find the point on the x-axis, which is equidistant from and .
• Find the area of a rhombus if its vertices are , , and taken in order.
• If the points A , B C and D form a parallelogram, find the value of a and height of the parallelogram taking AB as the base.
• Find a relation between x and y if the points A, B and C are collinear.
• Find the area of a triangle whose vertices are given as , and .
• If the distances of P from A and B are equal, then prove that 3x = 2y.
• In what ratio does the point divide the line segment joining the points P and Q? Also, find the value of y.

## Introduction To Coordinate Geometry

Coordinate geometry is defined as the study of geometry using the coordinate points. Using coordinate geometry, it is possible to find the distance between two points, dividing lines in m:n ratio, finding the mid-point of a line, calculating the area of a triangle in the Cartesian plane, etc. There are certain terms in Cartesian geometry that should be properly understood. These terms include:

Coordinate Geometry Terms
Coordinate Geometry DefinitionIt is one of the branches of geometry where the position of a point is defined using coordinates.
What are the Coordinates?Coordinates are a set of values which helps to show the exact position of a point in the coordinate plane.
Coordinate Plane MeaningA coordinate plane is a 2D plane which is formed by the intersection of two perpendicular lines known as the x-axis and y-axis.
Distance Formula
It is used to divide any line into two parts, in m:n ratio
Mid-Point TheoremThis formula is used to find the coordinates at which a line is divided into two equal halves.

## Mcq Questions For Class 10 Maths With Answers Chapter 7 Coordinate Geometry

#### MCQ Questions for Class 10 Maths with Answers Chapter 7 Coordinate Geometry with Answers

These MCQ Questions for Class 10 Maths Chapter 7 Coordinate Geometryare prepared according to the latest pattern. It is very helpful for students who wants to do quick revision of all the concepts related to linear equations.

#### Class 10 Maths Chapter 7 Coordinate Geometry MCQs

Q.1. The point on x-axis which is equidistant from the points A and B is

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## Draw The Graph Of X = 3 On A The Number Plane

Question Four2 marksWrite the equation of a line that has a gradient of 7 and a y intercept of -3__________________________________________________________________________

__________________________________________________________________________Question FiveThe straight line AB on a number plane has the endpoints A and B Find:a. the gradient of AB2 marksb. the length of AB as a surd

2 marks

c. the midpoint of AB

2 marks

Find the equation of this line

4 marks

REVISION NOTES for COORDINATE GEOMETRY1. Application of Pythagoras theoremc2 = a 2 + b 2

## Coordinate Geometry Practice Questions For Grade 10 PQRS is a rectangle formed by joining the points P, Q, R and S . A, B, C and D are the mid-points of PQ, QR, RS and SP respectively. Is the quadrilateral ABCD a square, a rectangle or a rhombus? Justify your answer. Solution

The area of a triangle is 5 sq.units. Two of its vertices are and . The third vertex is where y = x + 3 . Find the coordinates of the third vertex.

Find the area of a triangle formed by the lines 3x + y 2 = 0 , 5x + 2y 3 = 0 and 2x y 3 = 0 Solution

If vertices of quadrilateral are at A , B , C and D and its area is 72 sq.units. Find the value of k. Solution

Without using distance formula, show that points , , and are the vertices of a parallelogram. Solution

Find the equations of the lines, whose sum and product of intercepts are 1 and 6 respectively. Solution

The owner of a milk store finds that, he can sell 980 litres of milk each week at 14/litre and 1220 litres of milk each week at 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at 17/litre? Solution

Find the image of the point with respect to the line x + 3y = 7 assuming the line to be a plane mirror Solution

Find the equation of a line passing through the point of intersection of the lines 4x + 7y 3 = 0 and 2x 3y + 1 = 0 that has equal intercepts on the axes. Solution

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## Class 10 Maths Mcqs Chapter 7 Coordinate Geometry

1. The distance of the point P from the x-axis is 2

Explaination: Reason: The distance from x-axis is equal to its ordinate i.e., 3

2. The distance between the point P and Q is 4

Answer: bExplaination: Reason: The required distance = \^}=\sqrt=\sqrt=5\)

3. The points , and are collinear ifthe value of p is 3

Explaination: Reason: The points are collinear if area of = 0= \ 0 -5 p -10-3 + 4-4p = 0 -9p = +9 p = -1

4. The area of the triangle ABC with the vertices A, B and C is 63

Explaination: Reason: Area of ABC = \ = \ = \= \ = \ × 106 = 53 sq. units

5. The distance of the point from the origin is + ² + ² || + || \

Answer: dExplaination: Reason: Distance of from origin = \^}=\sqrt+\beta^}\)

6. The area of the triangle whose vertices are A, B and C is 11

Explaination: Reason: Required area= \= \= \ × 22 = 11

7. The line segment joining the points and is trisected. The coordinates of point of trisection are

Answer: bExplaination: Reason: Since the line segment AB is trisected

8. The line 3x + y 9 = 0 divides the line joining the points and internally in the ratio 3 : 4

Answer: aExplaination: Reason: Let the line 3x + y 9 = 0 divide the line segment joining A ad B in the ratio K : 1 at point C.

9. The distance between A and B is

10. If is the mid-point of the segment joining the points P and R, then the value of a is 12

## Practice Questions Using Coordinate Geometry Formulas

• Find the distance between two points and .
• Calculate the slope of a line with coordinates and .
• Calculate the area of a triangle ABC whose vertices are at A, B and C.
• Calculate the midpoint of the line segment joining the points P and Q
• Keep visiting BYJUS and get more such maths formulas and concept explanations for free. Also, download BYJUS- The Learning App to get video lessons on different maths topics.

Put your understanding of this concept to test by answering a few MCQs. Click Start Quiz to begin!

Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz

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## Examples Based On Coordinate Geometry Concepts

Examples 1: Find the distance between points M and N .

Solution:

Applying the distance formula we have,

\^}\)

\^} = \sqrt\)

Example 2: Find the equation of a line parallel to 3x+4y = 5 and passing through points .

Solution:

For a line parallel to the given line, the slope will be of the same magnitude.

Thus the equation of a line will be represented as 3x+4y=k

Substituting the given points in this new equation, we have

k = 3 × 1 + 4 × 1 = 3 + 4 = 7

Therefore the equation is 3x + 4y = 7

## Year 10 Mathematics Topic Test

Coordinate Geometry Practice Set 5.2 Class 10 Maharashtra Board New Syllabus Part 2

The gradient of y = 4x + 2 is1

Which of these lines has a gradient of 1A.

The graph of x = 0A. has zero gradient B. is the x-axis C. is the y axisQuestion Five

Which of these lines is not parallel to the other three?1

From the diagram below, the coordinates of the midpoint of AB arey

The length of the interval AB in the diagram below is2

Using the diagram in Question Eight the gradient of AB is ( the formula is2

Using the diagram below the y – intercept isy

Using the diagram in Question Ten the gradient of the line is2

Combining the answers of Question Ten and Question Eleven, the equation forthe line in Question Ten is3

A. y = 2 x + 3

Question ThirteenWhich line is parallel toA.

B. y = 2 x 2 C. y = 3 x

D. y = 3 x + 3

y =4?

Which of these points lies on the lineA.

3y + 3x = 3 can be rewritten as:A.

Complete the table of values for

y = 3x + 4

Write any equation of a straight line that has a y intercept of 4

2 marks

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## Cbse Practice Papers With Solution

Practice makes perfect. The more you practice the better you perform. CBSE practice question papers are based on NCERT syllabus and latest CBSE curriculum for this academic session. The unit tests, chapter wise solved papers, important questions, and questions asked in previous year exams are included in CBSE test papers and CBSE practice papers with solution and answer keys. The solved question papers from chapter 7 Coordinate Geometry have all type of questions may be asked in annual exams such as VSA very short answer type questions, SA short answer type questions, LA long answer type questions, VBA value based questions and HOTS higher order thinking skill based questions.

## Cbse Latest Practice Papers

CBSE India Board Sample Papers, CBSE Guess Papers, CBSE Practice Papers, NCERT Question papers, These Sample, Guess, Question Papers is designed by Expert Teachers of Various Central Board of Secondary Education Teachers for CBSE Students of India and abroad. It covers all the classes and all the subjects such as English, Hindi, Science, French, German, SST, Mathematics, Chemistry, Mathematics. Download all the CBSE Sample Papers, CBSE Guess Papers and CBSE Sample Question Papers from myCBSEguide.com

CBSE Test Papers for Class 12

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## Important Questions Class 10 Maths Chapter 7 Coordinate Geometry

Important Questions Class 10 Maths Chapter 7 Coordinate Geometry are given at BYJUS with stepwise solutions. Students who are preparing for the board exams of 2021-22 are advised to practice these important questions of Coordinate Geometry to score high marks in the Maths exam. These questions will provide good practice to students to solve any problem asked in the exam from this chapter. Solving these questions will also help in revision, and it will boost the confidence level of students.

This chapter has some important formulas to help students with their board exam preparation and competitive exams. Some of the important questions from the distance formula, section formula, and the triangle area are provided here. Students can also get the solutions for all the questions of the Class 10 NCERT textbook for Maths.

## Why Do We Need Coordinate Geometry Coordinate geometry has various applications in real life. Some of the areas where coordinate geometry is an integral part include.

• In digital devices like computers, mobile phones, etc. to locate the position of cursor or finger.
• In aviation to determine the position and location of airplanes accurately.
• In maps and in navigation .
• To map geographical locations using latitudes and longitudes.

Put your understanding of this concept to test by answering a few MCQs. Click Start Quiz to begin!

Select the correct answer and click on the Finish buttonCheck your score and answers at the end of the quiz

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## Cbse Test Papers Class 10 Mathematics Coordinate Geometry

CBSE chapter wise practice papers with solution for class 10 Mathematics chapter 7 Coordinate Geometry for free download in PDF format. 10th Mathematics chapter 7 Coordinate Geometry have many topics. All these topics are included in CBSE solved test papers of class 10 Mathematics chapter Coordinate Geometry. CBSE solved test papers and chapter wise question papers for practice with solution have plenty of questions for daily practice and smart study.

## Section Formula: To Find A Point Which Divides A Line Into M: N Ratio

Consider a line A and B having coordinates \\ \ \) & \\) respectively. Let P be a point that which divides the line in the ratio m:n, then the coordinates of the coordinates of the point P is given as-

• When the ratio m:n is internal:
• When the ratio m:n is external:

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## Mcq Questions For Class 10 Maths Coordinate Geometry With Answers

October 19, 2019 by Veerendra

Free PDF Download of CBSE Class 10 Maths Chapter 7 Coordinate Geometry Multiple Choice Questions with Answers. MCQ Questions for Class 10 Maths with Answers was Prepared Based on Latest Exam Pattern. Students can solve NCERT Class 10 Maths Coordinate Geometry MCQs with Answers to know their preparation level.

## Angle Formula: To Find The Angle Between Two Lines

Coordinate Geometry Practice Set 5.2 Class 10 Maharashtra Board New Syllabus Part 3

Consider two lines A and B, having their slopes to be \ respectively.

Let be the angle between these two lines, then the angle between them can be represented as-

Special Cases:

• Case 1: When the two lines are parallel to each other,

\ = m

Substituting the value in the equation above,

• Case 2: When the two lines are perpendicular to each other,

m1 . m2 = -1

Substituting the value in the original equation,

\ which is undefined.

= 90°

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## What Is A Co

You must be familiar with plotting graphs on a plane, from the tables of numbers for both linear and non-linear equations. The number line which is also known as a Cartesian plane is divided into four quadrants by two axes perpendicular to each other, labelled as the x-axis and the y-axis.

The four quadrants along with their respective values are represented in the graph below-

The point at which the axes intersect is known as the origin. The location of any point on a plane is expressed by a pair of values and these pairs are known as the coordinates.

The figure below shows the Cartesian plane with coordinates . If the coordinates are identified, the distance between the two points and the intervals midpoint that is connecting the points can be computed.

Coordinate Geometry Fig. 1: Cartesian Plane

## Coordinate Geometry Year 10 Int Math

Subject: Mathematics

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#### waynegretzky123

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This would be really good for revision or consolidating work on coordinate geometry. The worksheet contains questions are gradients, finding midpoints, rearranging equations to the form y = mx + c and more. Thank you for sharing.

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## Coordinate Geometry Questions For Practice

• Calculate the ratio in which the line 2x + y 4 = 0 divides the line segment joining the points A and B.
• Find the area of the triangle having vertices at A, B, and C which are at points , , and respectively. Also, mention the type of triangle.
• A point A is equidistant from B and C. Find the value for x and the distance BC.
• ## Cbse Question Papers 10th Mathematics Chapter 7 CBSE papers with answers and solutions for chapter Coordinate Geometry class 10th Mathematics includes practice question papers with 10-12 questions in each test paper. There are around 3-5 solved test papers in each chapter. Thus, users will get around 30-50 very important questions from each chapter in form of CBSE test papers with complete solution and answers. The question papers and CBSE with solutions practice papers for 10 Mathematics Coordinate Geometry are very helpful for students who wish to get good marks in exams.

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