Do you remember what a plane is? A plane is any flat surface which can go on infinitely in both of the directions. Now, if there is a point on a plane, you can easily locate that point with the help of coordinate geometry. Using the two numbers of the coordinate geometry, a location of any point on the plane can be found. Let us know more!
A coordinate geometry is a branch of geometry where the position of the points on the plane is defined with the help of an ordered pair of numbers also known as coordinates.
What are Coordinates?
Now, to help you understand the coordinates, take a look at the figure below.
Now, consider the grid on the right. The columns of the grid are labeled as A, B, C, D, E, F, etc. On the other hand, the rows are numbered as 1, 2, 3, 4, 5, 6, and so on. You can see that the letter X is located in the box D3 i.e. column D and row 3. Here, D and 3 are the coordinates of this box.
The box has two parts – one is the row and the other is the column. You need to understand that there are several boxes in every row and several boxes in every column. So, when you have both of them, you can find one single box that is the point where the rows and the columns intersect each other.
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The Coordinate Plane
In the coordinate geometry, all the points are located on the coordinate plane. Take a look at the figure below.
The figure above has two scales – One is the X-axis which is running across the plane and the other one is the y-axis which is at the right angles to the X-axis. This is similar to the concept of the rows and columns that we discussed in the first part above.
Understanding the Concept of Coordinates
- The point of intersection of the x and the y-axis is known as the origin. At this point, both x and y are 0.
- The values on the right-hand side of the x-axis are positive and the values on the left-hand side of the x-axis are negative.
- Similarly, on the y-axis, the values located above the origin are positive and the values located below the origin are negative.
- When you have to locate a point on the plane, it is determined by a set of two numbers. So, first, you have to write about its location on the x-axis followed by its location on the y-axis. Together, the two will determine a single and unique position on the plane.
So, in the figure above, the point A has a value 20 on the x-axis and value 15 on the y-axis. These are also the coordinates of the point A. Often these points are also regarded as the “rectangular coordinates”. Please note: The order of the points on the plane is crucial. You have to write the x coordinate ahead of the y coordinate.
Things That Have Been Made Possible By Coordinate Geometry
If you know the coordinates of a group of points, you can do the following:
- Determine the distance between these points.
- Find the equation, midpoint, and slope of the line segment.
- Determine if the given lines are perpendicular or parallel.
- Find the perimeter and the area of the polygon formed by the points on the plane.
- Transform the shape by reflecting, moving and rotating it.
- Define the equations of ellipses, curves, and circles.
Question For You
Question 1: What is the name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane?
Answer : The name of horizontal and vertical lines that are drawn to find out the position of any point in the Cartesian plane are determined by x-axis and y-axis respectively.
Question 2: Who is the father of coordinate geometry?
Answer: The father of coordinate geometry was René Descartes. He was referred to as the father of analytical geometry due to his contributions to the field. As his Latin name was Renatius Cartesius, thus we learn that the terms ‘Cartesian plane’ and ‘Cartesian coordinate system’ were a derivative of this man’s name.
Question 3: What do we need to coordinate geometry for?
Answer: Coordinate geometry is needed to offer a connection between algebra and geometry with the use of graphs of lines and curves. It is an essential branch of math and usually assists us in locating points in a plane. Moreover, it also has many uses in fields of trigonometry, calculus, dimensional geometry and more.
Question 4: What is Section Formula?
Answer: Section formula helps us knowing the coordinates of the points that are dividing a given line segment into two parts. This allows the lengths to be in the ratio m: n m: n m: n. Thus, the midpoint of a line segment is the point which divides a line segment into two equal halves.
Question 5: What is the definition of coordinate geometry in math?
Answer: Coordinate geometry refers to the study of algebraic equations on graphs. Moreover, if we look at its example, it is plotting points, lines and curves on an x and y-axis.