The position of a point in a plane is provided by the coordinates on the graph. XOX’ and YOY’ are the two intersecting and perpendicular lines. We know that x-axis and y-axis divide the XY-plane into four parts known as quadrants. The position of a point in the plane is defined with the help of ordered pairs. Let us discuss more about the position of a point in a plane from this article. Scroll down this page to practice the examples problems on the position of a point in the plane from the chapter reflection.
Also Go through:
- Reflection of a Point in the y-axis
- Reflection of a Point in the Origin
- Reflection of a Point in the x-axis
Position of a Point in a Plane
The position of a point in the plane is expressed by a set of values or numbers called coordinates. There are two coordinates in the geometry they are x-coordinate known as abscissa and y-coordinate known as ordinate. Any point in a plane is referred to by a point (x, y), where the x-value is the position of the point with reference to the x-axis and the y-value is the position of the point with reference to the y-axis.
Position of a Point in a Plane Examples
Check out the problems given in the below section to understand in depth about the position of a point in a plane.
Example 1.
Find the position of a point in a plane (2,4).
Solution:
Given that the point is (2,4)
Consider the point (2,4) has A.
Plot the point A(2,4) in the first quadrant takes a distance of 2 from the x-axis and 4 from the y axis.
So, the coordinates of A are (2, 4). We express it by writing A = (2, 4).
And also consider B, C, and D are also points in the other quadrant whose distance from the y-axis and the x-axis are the same point. But due to their positions in different quadrants, their coordinates are different. Thus, the coordinates of B, in the second quadrant, are (-2, 4), and C is the third quadrant, are (-2, -4) and D is the fourth quadrant, are (2, -4).
Example 2.
Find the position of a point in a plane (6,7).
Solution:
Given that the point is (6,7)
Consider the point (6,7) has A.
Plot the point A(6,7) in the first quadrant takes a distance of 6 from the x-axis and 7 from the y axis.
So, the coordinates of A are (6, 7). We express it by writing A = (6, 7).
And also consider B, C, and D are also points in the other quadrant whose distance from the y-axis and the x-axis are the same point. But due to their positions in different quadrants, their coordinates are different. Thus, the coordinates of B, in the second quadrant, are (-6, 7), and C is the third quadrant, are (-6, -7) and D is the fourth quadrant, are (6, -7).
Example 3.
Find the position of a point in a plane (12,14).
Solution:
Given that the point is (12,14)
Consider the point (12,14) has A.
Plot the point A(12,14) in the first quadrant takes a distance of 12 from the x-axis and 14 from the y axis.
So, the coordinates of A are (12, 14). We express it by writing A = (12, 14).
And also consider B, C, and D are also points in the other quadrant whose distance from the y-axis and the x-axis are the same point. But due to their positions in different quadrants, their coordinates are different. Thus, the coordinates of B, in the second quadrant, are (-12, 14), and C is the third quadrant, are (-12, -14) and D is the fourth quadrant, are (12, -14)
Example 4.
Find the position of a point in a plane (5,10).
Solution:
Given that the point is (5,10)
Consider the point (5,10) has A.
Plot the point A(5,10) in the first quadrant takes a distance of 5 from the x-axis and 10 from the y axis.
So, the coordinates of A are (5, 10). We express it by writing A = (5, 10).
And also consider B, C, and D are also points in the other quadrant whose distance from the y-axis and the x-axis are the same point. But due to their positions in different quadrants, their coordinates are different. Thus, the coordinates of B, in the second quadrant, are (-5, 10), and C is the third quadrant, are (-5, -10) and D is the fourth quadrant, are (5, -10).
Example 5.
Find the position of a point in a plane (2,9).
Solution:
Given that the point is (2,9)
Consider the point (2,9) has A.
Plot the point A(2,9) in the first quadrant takes a distance of 2 from the x axis and 9 from the y axis.
So, the coordinates of A are (2, 9). We express it by writing A = (2, 9).
And also consider B, C, and D are also points in the other quadrant whose distance from the y-axis and the x-axis are the same point. But due to their positions in different quadrants, their coordinates are different. Thus, the coordinates of B, in the second quadrant, are (-2, 9), and C is the third quadrant, are (-2, -9) and D is the fourth quadrant, are (2, -9).
FAQs on Position of a Point in a Plane
1. What is the position of a plane?
A plane is a surface in which any two points are taken and the straight line drawn to join these two points that lie within that plane or surface.
2. What is the first coordinate of a point?
If the coordinates points are (a,b). The first point named in the ordered pair is called x-coordinate and the second is called the y-coordinate.
3. How many points determine a line?
If any two distinct points in a plane determine a line, and the equation is also determined by the coordinates of the points.