Question
What is the line of reflection for 
and its image?
- x-axis
- y-axis
- y = x
- y = -x
Hint:
Observe the graph and find the equation for the line of graph.
The correct answer is: x-axis
* In Geometry, a reflection is known as a flip. A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection.
*It is a type of transformation that produces mirror image of the shape.
* Matrix representation is the efficient way for the transformation of points.
* Every vertex is placed in columns.
Given That:
>>>From Figure:
The coordinates A(2,3); B(6,1); C(7,5) after reflection became A'(2,-3);B'(6,-1);C'(7,-5).
>>>We can observe that the x-coordinate remains same(a=a) and y-coordinate changes sign with equal magnitude(b=-b).
>>>Therefore, we can say that point (a, b) is changed to (a, -b).
>>>This can be done by reflecting a point using x-axis.
>>>Therefore, the line of reflection becomes x-axis.
From the graph, the line of reflection is x-axis.
Related Questions to study
Find the reflection matrix on the y- axis.
The matrix representation for the reflection with respect to y-axis:
Find the reflection matrix on the y- axis.
The matrix representation for the reflection with respect to y-axis:
Write the matrix for the polygon.
The required matrix is:
Write the matrix for the polygon.
The required matrix is:
Write the matrix for the polygon.
The required matrix is:
Write the matrix for the polygon.
The required matrix is:
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect 
in the y - axis.
The required matrix is:
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect in the y - axis.
The required matrix is:
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect
in the x - axis.
>>>Since, it is reflected on x-axis, the matrix multiplication looks like:
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect
in the x - axis.
>>>Since, it is reflected on x-axis, the matrix multiplication looks like:
Find point C on the x-axis, so AC + BC is minimum.
A(4, -3), B (8, -5)
>>>Finding A'B line AB' line intersection point gives the point that gives minimum sum of AC and BC on x-axis.
>>>Therefore, the point of intersection becomes: C(5.5,0).
Find point C on the x-axis, so AC + BC is minimum.
A(4, -3), B (8, -5)
>>>Finding A'B line AB' line intersection point gives the point that gives minimum sum of AC and BC on x-axis.
>>>Therefore, the point of intersection becomes: C(5.5,0).
Find point C on the x-axis, so AC + BC is minimum.
A(2, 4), B (6, 2)
The point present in the x-axis. and also on the line image of A and point B.
>>>From the given data the point becomes (4.7,0)
Find point C on the x-axis, so AC + BC is minimum.
A(2, 4), B (6, 2)
The point present in the x-axis. and also on the line image of A and point B.
>>>From the given data the point becomes (4.7,0)
What is the line of reflection for and its image?
From the graph, the line of reflection is x= -1
What is the line of reflection for and its image?
From the graph, the line of reflection is x= -1
What is the line of reflection for and its image?
From the graph, the line of reflection is y-axis.
What is the line of reflection for and its image?
From the graph, the line of reflection is y-axis.
What is the line of reflection for and its image?
From the graph, the line of reflection is y = x.
What is the line of reflection for and its image?
From the graph, the line of reflection is y = x.
Find the reflection matrix on the x-axis.
The reflection matrix on the x-axis = 
Find the reflection matrix on the x-axis.
The reflection matrix on the x-axis =
Write the matrix for the polygon.
From the graph, the coordinates of polygon are A(0, 2), B(0, 4), C(3, 5), and D(3, 1)
Write the matrix for the polygon.
From the graph, the coordinates of polygon are A(0, 2), B(0, 4), C(3, 5), and D(3, 1)
Find the image coordinates of the triangle ABC, if A (-4,0), B (-3,3) and C (-1,2), which is reflected along y-axis.
If (a, b) is reflected in the y-axis, its image is the point (-a, b).
(a, b) → (-a, b)
A (-4, 0) → A’ (4, 0)
B (-3, 3) → B’ (3, 3)
C (-1, 2) → C’ (1, 2)
Image coordinates of the triangle ABC are A’ (4, 0), B’ (3, 3) and C’ (1, 2).
Find the image coordinates of the triangle ABC, if A (-4,0), B (-3,3) and C (-1,2), which is reflected along y-axis.
If (a, b) is reflected in the y-axis, its image is the point (-a, b).
(a, b) → (-a, b)
A (-4, 0) → A’ (4, 0)
B (-3, 3) → B’ (3, 3)
C (-1, 2) → C’ (1, 2)
Image coordinates of the triangle ABC are A’ (4, 0), B’ (3, 3) and C’ (1, 2).
Find the image coordinates of the line AB, if A (6, 4) and B (6,1), which is reflected along y = -x
If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
(a, b) → (b, a)
A(6, 4) → A’(-4, -6)
B (6,1) → B’(-1, -6)
Image of the line A’( -4, -6), B’( -1, -6)
Find the image coordinates of the line AB, if A (6, 4) and B (6,1), which is reflected along y = -x
If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
(a, b) → (b, a)
A(6, 4) → A’(-4, -6)
B (6,1) → B’(-1, -6)
Image of the line A’( -4, -6), B’( -1, -6)
Find the image coordinates of the line AB, if A (6, 4) and B (6, 1), which is reflected along y = x
If (a, b) is reflected in the line y = x, its image is the point (b, a).
(a, b) → (b, a)
A (6, 4) → A’ (4, 6)
B (6, 1) → B’ (1, 6)
Image of line A’ (4, 6), B’ (1, 6)
Find the image coordinates of the line AB, if A (6, 4) and B (6, 1), which is reflected along y = x
If (a, b) is reflected in the line y = x, its image is the point (b, a).
(a, b) → (b, a)
A (6, 4) → A’ (4, 6)
B (6, 1) → B’ (1, 6)
Image of line A’ (4, 6), B’ (1, 6)
