Problems on Reflection in the x-axis or y-axis are provided here. So, the students who are searching for the answer key of reflection in maths can get them on this page. Let us discuss different types of questions on How to Reflecti Over the x-axis or y-axis. Know what is meant by reflection and reflection in the x-axis and y-axis from the previous articles. Click on the below links to learn the concepts of reflection.
Also Read:
- Reflection of a Point in the x-axis
- Reflection of a Point in the y-axis
Reflection in the x-axis or y-axis Questions and Answers
Example 1.
Point A (3, -2) is reflected as A’ in the y-axis. Point B on reflection in the x-axis is mapped as B’ (-1, 6). Write down the coordinates of A’ and B.
Solution:
Given that
Reflection in y-axis is given by My (x, y) = (-x, y)
A’ = Reflection of A(3, -2) in y-axis = (-3, -2)
Reflection in x-axis is given by Mx (x, y) = (x, -y)
B’ = Reflection of B in x-axis = (-1, 6)
Thus, B = (-1, -6)
Example 2.
The point (-4, 0) on reflection in a line is mapped as (4, 0) and the point (-2, -3) on reflection in the same line is mapped as (2, -3).
(a) Name the line of reflection.
(b) Write down the coordinates of the image of (5, -7) in the line obtained in (a).
Solution:
Given that
(a) We know that reflection in line x = 0 is the reflection in the y-axis.
It is given that:
Point (-4, 0) on reflection in a line is mapped as (4, 0).
Point (-2, -3) on reflection in the same line is mapped as (2, -3).
Hence, the line of reflection is x = 0.
(b) It is known that My (x, y) = (-x, y)
Coordinates of the image of (5, -7) in the line x = 0 are (-5, -7).
Example 3.
P and Q have coordinates (-1, 3) and (8, 4) respectively. Reflect P in the x-axis to P’ and Q in the y-axis to Q’. State the coordinates of P’ and Q’.
Solution:
Reflection in x-axis is given by Mx (x, y) = (x, -y)
P’ = Reflection of P(-1, 3) in x-axis = (-1, -3)
Reflection in y-axis is given by My (x, y) = (-x, y)
Q’ = Reflection of Q(8, 4) in y-axis = (-8, 4)
Thus, the coordinates of points P’ and Q’ are (-1, -3) and (-8, 4) respectively.
Example 4.
A point P is reflected in the x-axis. Coordinates of its image are (-5, 5).
(i) Find the coordinates of P.
(ii) Find the coordinates of the image of P under reflection in the y-axis.
Solution:
Given that
(i) Since, Mx (-5, -5) = (-5, 5)
So, the coordinates of P are (-5, -5).
(ii) Coordinates of the image of P under reflection in the y-axis (5, -5).
Example 5.
The point P (x, y) is first reflected in the x-axis and reflected in the origin to P’. If P’ has coordinates (-9, 5); evaluate x and y.
Solution:
Mx (x, y) = (x, -y)
MO (x, -y) = (-x, y)
Thus, we get the coordinates of the point P’ as (-x, y). It is given that the coordinates of P’ are (-9, 5).
On comparing the two points, we get,
x = 9 and y = 5
Example 6.
The point (a, b) is first reflected in the origin and then reflected in the y-axis to P’. If P’ has coordinates (3, 4); evaluate a and b.
Solution:
MO (a, b) = (-a, -b)
My (-a, -b) = (a, -b)
Thus, we get the coordinates of the point P’ as (a, -b). It is given that the coordinates of P’ are (3, 4).
On comparing the two points, we get,
a = 3 and b = -4
Example 7.
Find the coordinates of the points (-6, 0) under reflection in the line y = 0
Solution:
Given that (4, 8)
The coordinate of the given point under reflection in the x-axis is (4, -8).
Example 8.
Find the coordinates of the points (3,7) under reflection on the x-axis.
Solution:
Given that (3, 7)
The coordinate of the given point under reflection in the x-axis is (3, -7).
Example 9.
Find the coordinates of the points (-4, 0) under reflection in the line y = 0
Solution:
Given that
(-4, 0)
The coordinate of the given point under reflection in the line y = 0 is (-4, 0).
Example 10.
Find the coordinates of the points (4,8) under reflection on the x-axis.
Solution:
Given that (4, 8)
The coordinate of the given point under reflection in the x-axis is (4, -8).