CBSE Class 10 Maths Important Questions on Chapter 7 - Coordinate Geometry

Students looking to find important questions for coordinate geometry can find it here in this article at the Vedantu website which is free and easily available for the student. The website allows for easy access to its important questions and also it is easily downloadable. Students will find these notes to be helpful during the preparation of their examinations, these important questions are easily downloadable in a pdf format. Students who find it difficult to study on the screen can also print this material so they don't waste too much time on the internet. These questions can come for more marks than what is anticipated and so students need to be thorough with their preparation. Class 10 board examination is an important one for students and students need to know how to prepare well for it so they can do well because the marks they score in 10th will carry on for life long. So students need to prepare early and have continuous revisions and to help them with that they can use this article which will help guide them through this chapter on coordinate geometry.

Important Topics Covered under CBSE Class 10 Maths Chapter 7 - Coordinate Geometry 

Coordinate geometry draws the linkage between geometry and algebra using various graphs and lines. Some of the concepts covered in this chapter are as follows

History of Coordinate Geometry 

Coordinate geometry was first introduced by a French mathematician known as Rene Descartes; he was the first person to find a method to describe the location of points. Later in his research, he concluded that different curves and lines could be found using equations using coordinate geometry. He was the first person to draw the link between geometry and algebra. His work was considered extremely useful and to honour his work the coordinates of a point are called cartesian coordinates and the coordinate plane is known as the cartesian coordinate plane.

Coordinates 

Coordinates are simply the various points on the plane. Using the x-axis and y-axis we can find out the exact location of the point. Because we are using a grid system it is much easier to locate anything because we just need to identify which cell( the intersection of rows and columns) the point falls.

Coordinate Plane 

In coordinate geometry, there is a coordinate plane where different points are placed. There are usually two different scales- one with right angles to it is known as the y axis and the one running across from the plane is known as the x-axis. The point of origin is where both the x and y-axis meet and are known as the point of origin, this is usually at point 0. 

Co coordinate geometry is quite simple, it uses pairs of numbers to give the location of a point on a plane.

Advantages of Coordinate Geometry 

When we know the coordinates of certain points we can do the following- Determine the distance between them

• We can find the equation, slope, and midpoint of any line segment.

• We can find whether the lines are perpendicular or parallel.

• Using the points we can find the perimeter and areas of any polygon.

• By Reflecting, moving, and rotating we can transform any shape. 

• Define various eclipses, curves, and circles. 

• Find out the distances between different points, lines, and shapes.

Class 10 Maths Chapter 7 Important Questions 

This chapter introduces students to coordinate geometry and students can study from this subject the very basics and get to a more intermediate level. The following are the important questions that students must look at when preparing for their examinations- 

1. There are two routes to use to travel from destination A to destination B. First Bus reaches via point C and the second bus reaches from A to B Directly. If Coordinates of A, B, and C are (-2,-3),(2,3), and (3,2) respectively then which bus do you want to travel from A to B? which value is depicted in the question.

2. On a sports day celebration, Shyam and Ram are standing at positions A and B and their coordinates are (2,-2) and (4,8). The teachers ask Pooja to fix the flag at the midpoint of the line joining points A and B. Find the coordinates of the midpoint? Which type of value would you infer from the question? 

3. To raise awareness of the hazard of smoking and the harm it does to the body, a school decided to start a “ no smoking” campaign. 10 students are asked to prepare campaign flags in the shape of a triangle. If the costs of 1cm2 of each banner are 2 rupees then find the overall cost incurred in the campaign. Which value is depicted in the question? 

4. Find the area of a rhombus if its vertices are (3,0), (4,5),(-1,4) and (-2,-1) taken in the area.

5. Find the centroid of a triangle whose vertices are(4,-8), (-9,7), and (8, 13). 

6. Prove that in a right-angled triangle the midpoint of the hypotenuse is in equal distance from all its vertices 

7. Prove that the diagonals of a rectangle bisect each other are all equal.

8. The length of a line segment is 10. If one endpoint (2,-3) and the abscissa of the second endpoint is 10 shows that the ordinate is 3 or -9.

9. Using section formulas show that points (-1,2),(5,0) and (2,1) are collinear.

10. Find the relation between x and y such that point (x,y) is equidistant from the points (7,1) and (3,5).

Some Practice Questions on CBSE Class 10 Maths Chapter 7 - Coordinate Geometry

1. (2a, a – 7) is the centre of a given circle. If the circle is passing through the point (11, –9) and it has a diameter of 10√2 units, then determine the value of a.

2. Are the points (1, 7), (4, 2), (–1, –1), and (– 4, 4) the vertices of a square? Explain why.

3. Determine a point on the x-axis that is equidistant from (2, –5) and (–2, 9).

4. Determine the ratio in which the line segment joining the points (8, –9) and (2, 1) is divided into by the line 2x + 3y – 5 = 0. Also, determine the coordinates of this point of division.

5. If the vertices of a rhombus are (3, 0), (4, 5), (– 1, 4), and (– 2, – 1), when taken in order, then determine its area. [Hint: Area of a rhombus = 1/2 (product of its diagonals)]

6. The distances of P(x, y) from A(5, 1) and B(-1, 5) are equal. Prove that 3x = 2y.

7. What ratio is the line segment joining the points P(2, -2) and Q(3, 7) divided by the point (24/11, y)? Also, determine the value of y.

8. The points A (1, –2), B (2, 3) C (a, 2) and D (– 4, –3) form a parallelogram. Determine the value of a and the height of this parallelogram, by considering AB to be the base.

9. The vertices of a triangle are (1, -1), (-4, 6), and (-3, -5). Determine its area.

10. The points A(x, y), B(-4, 6), and C(-2, 3) are collinear. Find a relation between x and y.

Benefits of Class 10 Maths Chapter 7 Important Questions

Mathematics can be quite a difficult subject to understand by yourself. So by using the right guide material like the ones found in Vedantu students can utilise it to their maximum and score the best marks possible. A lot of this subject is a theory so students need to just understand the various concepts and don't have to mug up anything like science subjects. 

• Students can use this text to use their time wisely, it helps boost their confidence after consistent practice and students can plan their preparation accordingly.

• Students can utilise and practise the important questions so that they can ace their examinations. 

• It provides students with a structure with which they will study for his or her upcoming examinations.

• This is a fundamental subject for high school kids and plays an important role in higher studies.

• Students don’t need to worry about the relevance of these questions as they're all cross-checked and updated consistently with the newest CBSE guidelines and rules. Therefore, the information in Vedantu is genuine and reliable.

• Students studying this chapter on coordinate geometry will find that it helps in higher studies and helps them understand the basics in any design engineering field.

Conclusion 

Mathematics is known to be a difficult subject. Coordinates are simply the various points on a plane. Using the x-axis and y-axis we can find out the exact location of the point. students will learn how to use various coordinate plans and different ways to locate points, lines, curves, and shapes. Students can use this article to use their time wisely, it helps boost their confidence after consistent practice and students can plan their preparation accordingly. Students can work more diligently towards their goals and strive for higher marks as well. These important questions make sure that students are aware of the various topics in the subject and learn to master all the concepts. This chapter teaches students to coordinate geometry in mathematics the questions provided in this article helps students understand the subject better.

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