Question
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect
in the x - axis.
Hint:
Multiply the reflection matrix with the matrix of real coordinates to obtain the matrix of image coordinates and then plot the graph.
The correct answer is:
* 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.
>>>Given That:
Use matrix multiplication to find the image. Graph the polygon and its image. Reflect in the x - axis.
>>>let (a, b) be a point in the plane. Then, the point of reflection with respect to x-axis is (a,-b).
* We know that reflection matrix on the x-axis: 
* Multiply the polygon matrix by the matrix for a reflection on the x-axis.
>>The required Graph:
>>>Since, it is reflected on x-axis, the matrix multiplication looks like:
Related Questions to study
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)
Graph the reflection of the polygon in the given line: 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) → (4, 6)
B (-5, -1) → (1, 5)
C (-3, -2) → (2, 3)
Graph the reflection of the polygon in the given line: 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) → (4, 6)
B (-5, -1) → (1, 5)
C (-3, -2) → (2, 3)
Graph the reflection of the polygon in the given line: 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) → (-4, -6)
B (-5, -1) → ( -1, -5)
C (-3, -2) → (-2, -3)
Graph the reflection of the polygon in the given line: 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) → (-4, -6)
B (-5, -1) → ( -1, -5)
C (-3, -2) → (-2, -3)
The vertices of a triangle are A (2, 3), B (6, 1) and C (7, 5). Graph the reflection of the triangle ABC in the given line y = 3
Point A is on the line, so its reflection is also on the same line (2, 3)
Point B is 2 units below the line, so its reflection is 2 units above the line at B’ (6, 5).
Point C is 2 units above the line, so its reflection is 2 units below the line at C’ (7, 1).
The vertices of a triangle are A (2, 3), B (6, 1) and C (7, 5). Graph the reflection of the triangle ABC in the given line y = 3
Point A is on the line, so its reflection is also on the same line (2, 3)
Point B is 2 units below the line, so its reflection is 2 units above the line at B’ (6, 5).
Point C is 2 units above the line, so its reflection is 2 units below the line at C’ (7, 1).
The vertices of a triangle are A(2,3), B (6,1) and C(7,5). Graph the reflection of the triangle ABC in the given line x-axis.
Point A is 2 units above the line, so its reflection is 2 units below the line at A’ (2, -3).
Point B is 1 unit above the line, so its reflection is 1 unit below the line at B’ (6, -1).
Point C is 5 units above the line, so its reflection is 5 units below the line at C’ (7, -5).
The vertices of a triangle are A(2,3), B (6,1) and C(7,5). Graph the reflection of the triangle ABC in the given line x-axis.
Point A is 2 units above the line, so its reflection is 2 units below the line at A’ (2, -3).
Point B is 1 unit above the line, so its reflection is 1 unit below the line at B’ (6, -1).
Point C is 5 units above the line, so its reflection is 5 units below the line at C’ (7, -5).
Graph the image of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), 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 (-4, 0) → A’(0,4)
B(-3, 3) → B’(-3, 3)
C(-1, 2) → C’(-2, 1)
Image coordinates of the triangle ABC are A’(0,4), B’(-3, 3) and C’(-2, 1).
Graph the image of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), 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 (-4, 0) → A’(0,4)
B(-3, 3) → B’(-3, 3)
C(-1, 2) → C’(-2, 1)
Image coordinates of the triangle ABC are A’(0,4), B’(-3, 3) and C’(-2, 1).
