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Exercise 7. Find the distance between the following pairs of points: i 2, 3 , 4, 1 ii -5, 7 , -1, 3 iii a, b , -a, -b Solution:. Find the distance between the points 0, 0 and 36, Determine if the points 1, 5 , 2, 3 and -2, are collinear. Check whether 5, -2 , 6, 4 and 7, -2 are the vertices of an isosceles triangle. In a classroom, 4 friends are seated at the points A, B, C and D as shown in the given figure.
Using distance formula, find which of them is correct. Name the type of quadrilateral formed, if any, by the following points, and give reasons for your answer.
Find the point on the x-axis which is equidistant from 2, -5 and -2, 9. Find the values of y for which the distance between the points P 2, -3 and Q 10, y is 10 units.
If Q 0, 1 is equidistant from P 5, -3 , and R x, 6 , find the values of x. Also, find the distances QR and PR. Find a relation between x and y such that the point x, y is equidistant from the points 3, 6 and -3, 4. Area of Triangle. It will let us find the area of any triangle in terms of coordinates of its vertices. This formula will also be used in finding the area of quadrilaterals.
All the basic formulas of coordinate geometry will help you to solve your geometry and algebra problems. Chapter 7 maths Class 10 provides you the list of all formulas of coordinate geometry to solve all the related problems.
General Form of a Line. Where A , B, C are real numbers and x and y are variables. Slope Intercept Form of a Line. Where x and y are variables, c is constant and m is the slope. Point-Slope Form. The slope of a Line Using Coordinates. The slope of a Line Using General Equation. Intercept-Intercept Form. Distance between two points O x 1, y 1 and B x 2, y 2. For Parallel Lines,. For Perpendicular Lines,. Angle between Two Lines. Area of a Triangle. Perpendicular Distance from a Point to a Line.
It is very important to get acquainted with these basic formulas of coordinate geometry. Chapter 7 Maths Class 10 coordinate formulas have been proven very helpful for students to solve the problems at a competitive level. Historical Facts. Rene Descartes, the Great French Mathematician of the seventeenth century, liked to lie in bed and think.
One day, when lying in the bed he solved the problem of describing the position of a point in a plane. His method was based on the old concept of latitude and longitude. Rene Descartes , a French Mathematician, came up with a system known as the cartesian coordinate system to describe the positions of points and lines in a plane. His latin name was Renatius Cartesius, hence the name cartesian plane was derived. He was referred to as the father of analytical geometry.
Through cartesian coordinate or rectangular coordinate system, we can study the problems involving both geometry and algebra,.
Cartesian geometry is also termed as analytic geometry. Today it is strongly believed that success comes from regular practice. Intelligence also sometimes fails if not practiced.
Maths needs a regular practice for perfection. Some people think Maths as a very tough subject, but if they have a regular practice of solving the problems they can crack any problem. Regular practice reduces the silly mistakes done during the examinations. Practising lots of problems makes you aware of all the possible questions related to any topic.
It makes it easier to solve any problem during your final exams. NCERT syllabus is designed according to the caliber of the students. Practicing NCERT problems after understanding the concept makes the students more confident in that area. Practicing not only improves your conceptual understanding but also improves your logical reasoning.
Understanding the concept thoroughly and then solving the NCERT question will definitely increase your score in examinations. Improves your accuracy. Makes the concepts more clear. Increases your speed.
It improves your logical reasoning. It makes you more confident in a particular area. Vedantu is a team of expert teaching professionals. Vedantu always tries to make the learning of any concept at the student level easy to understand. It explains the concept stepwise and more precisely along with the pictorial representation of the concept. Vedantu is a strong believer to impart quality education to students.
NCERT solutions are given in simple language with alternate solutions and diagrammatic representation for easy understanding of the problem. Along with these Vedantu tries to make the learning fun by lowering the pressure of studies. The solutions are divided into parts so that they can be easily understood by the students. The explanation is given in stepwise format. All the solutions are given at the student's level of understanding.
The solutions are precise, brief and with relevant diagrams. They are given in proper stepwise format along with the necessary comments. The solutions are properly formatted to reduce the unnecessary burden of lengthy solutions. Vedantu is a No. It also has the potential to help you score more in the examination. Vedantu tries their level best to provide quality education, by providing NCERT solutions for coordinate geometry Class It also provides more practice questions for bringing the perfection in the concepts.
And they will be very helpful in the examination. Keep this Vedantu NCERT solution handy so that there will be no inconvenience during your study of coordinate geometry. Why is Coordinate Geometry Important? Coordinate geometry helps you to locate the exact location of a point in a plane.
Coordinate geometry provides us the link between algebra and geometry through lines, graphs, curves and equations. Coordinate geometry Class 10 holds a weightage of total 6 marks in the final board examination. Coordinate geometry basically explains four concepts introduction to coordinate geometry, distance formula, section formula and area of triangle.
Deeper into Exercises. Each exercise is solved by vedantu experts. Every concept is followed by well defined exercises. Exercises are aimed to test your conceptual knowledge. All the problems of the exercises are based on the concepts explained earlier. Every problem has a step wise explanation. Students can easily understand the concept used behind the problems.
Different types of problems are given to understand the concept thoroughly. Vedantu has studied all the exercise and variety of problems involved in each exercise.
Exercise one is based on how to find distance between two points given on a plane. By the end of this exercise the student will be able to find the distance between two points. With this property there are different types of problems in the exercise 7.
We can calculate the distance between points and prove the types of triangle are isosceles, equilateral or types quadrilateral square, rhombus, rectangle or whether the points are collinear or not. Vedantu provides step wise solutions for every problem with relevant diagrams. Diagrams help us visualize the problem. With the distance formula we can even find the unknown values of x and y coordinate if the distance between the two points are given. Vedantu provides a stepwise explanation of the solution so that you can solve any similar problems..
Section formula is derived by a well defined theorem. It is basically given on four types of problems. Type1: Finding the section ratio or the end points of the segment when the section point is given.
Type 2: Finding the section point when the section ratio is given. Type 3: Determination of the type of a given quadrilateral.
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