Hello Students!!! Are you excited and interested to know in-depth about reflection? Don’t worry we are here to help you to give detailed information about the reflection of a point in the origin, x-axis, y-axis, and so on. We know that point reflection is a type of reflection. Know how to find the coordinates of the reflection of the point in the origin from this article. The image of the point (p, q) in the origin is the point (-p, -q).
Read Article:
- Reflection of a Point in the y-axis
- Reflection of a Point in the x-axis
- Worksheet on Reflection in the Origin
Reflection of a Point in the Origin
In order to locate the coordinates in the contiguous figure, the origin represents the plane mirror. Let X be any point in the first coordinates (h, k). M’ is the reflected point in the origin formed by the third quadrant whose coordinates will be (-h, -k). To find the reflection of a point in the origin are have to change the signs of the x-coordinates and y-coordinates.
By seeing the above figure we can say that X'(-h, -k) is the mirror image of X(h, k).
Rules to find the Reflection of a Point in the Origin
To find the reflection of the point in the origin there are some rules to follow.
i. Change the sign of the x-coordinate i.e., abscissa.
ii. Change the sign of the y-coordinate.
Reflection of a Point in the Origin Solved Problems
Example 1.
What is the reflection of the point A(2, 5) in origin?
Solution:
Given that A(2,5)
The reflection of the point A (2, 5) is P’ (-2, -5).
Example 2.
What is the reflection of the point B(-6, -9) in the origin?
Solution:
Given that B(-6,-9)
The reflection of point B (-6, -9) is B’ (6, 9).
Example 3.
What is the reflection of the point C(-3,8) in the origin?
Solution:
Given that C(-3,8)
The reflection of point C (-3, 8) is C’ (3, -8).
Example 4.
What is the reflection of the point D(1, -1) in the origin?
Solution:
Given that D(1,-1)
The reflection of the point D(1,-1) is C'(-1, 1)
Example 5.
What is the reflection of the point E(5,-1)
Solution:
Given that E(5,-1)
The reflection of the point S (5, -1) is S’ (-5, 1).
FAQs on Reflection of a Point in the Origin
1. What does reflection in the origin mean?
When you reflect a point in the origin, both the x-coordinate and the y-coordinate change their signs. In a point reflection in the origin, the image of the point (x,y) is the point (-x,-y).
2. Which functions have graphs that are symmetrical with respect to the origin?
A function that is symmetrical with respect to the origin is called an odd function. f(x).
Since f(−x) = f(x), this function is symmetrical with respect to the y-axis.
3. What is the rule for reflection?
If you reflect a point across the line y = x, the x-coordinate, and y-coordinate change places.
If you reflect over the line y = -x, the x-coordinate and y-coordinate change places.
The line y = x is the point (y, x). the line y = -x is the point (-y, -x).