We will discuss here how to find the reflection of a point in the origin.
Let M (a, b) be any point in the coordinate plane and O be the origin. Now join M and O, and produce it to the point M’ such that M’O = OM. Then the point M’ is the reflection of the point M in the origin. Thus, M’ is the image of M in the origin O. From the figure, we find that the coordinates of the point M’ are (-a, -b).
Thus, the reflection of the point M (a, b) in the origin is the point M’ (-a, -b)
Or
The image of the point (a, b) in the origin is the point (-a, -b).
Symbolically M \(_{o}\) (a, b) = (-a, -b).
Rules to find the
reflection of a point in the origin:
(i) Change the sign of x-coordinate i.e. abscissa.
(ii) Change the sign of y-coordinate i.e. ordinate.
For example:
(i) Reflection of the point (5, 6) in the origin is the point (-5, -6) i.e. M \(_{o}\) (5, 6) = (-5, -6)
(ii) Reflection of the point (7, -3) in the origin is the point (-7, 3) i.e. M \(_{o}\) (7, -3) = (-7, 3)
Solved examples to find the reflection of a point in the origin:
Find the points onto which the following points are mapped on reflection in the origin.
(i) (4, 9)
(ii) (-1/4, 1/6)
(iii) (10, -15)
(iv) (-a, -b)
Solution:
We know that a point (x, y) is mapped onto the point (-x, -y) on reflection in the origin.
(i) (4, 9) maps onto (-4, -9)
(ii) (-1/4, 1/6) maps onto (1/4, -1/6)
(iii) (10, -15) maps onto (-10, 15)
(iv) (-x, -y) maps onto (x, y)
● Reflection
10th Grade Math
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