Question
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
Hint:
Plot the points on the graph and then obtain the points of reflections.
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.
The reflection transformation can be done in many ways.
*Reflection over X-axis
*Reflection over Y-axis
*Reflection over Y = X
Given That:
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
>>>let (a, b) be a point in a x-y plane and then, the point of reflection becomes x+2(distance).
>>>Therefore, the point of reflection for the vertices of a triangle A (2, 3), B (6, 1) and C (7, 5):
A'(2,3+2(3-3)); B'(6,1+2(3-1)); C'(7,5-2(5-3));
= A'(2,3); B'(6,5); C'(7,9)
>>>Then, the required graph:
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).
Related Questions to study
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).
Find the image coordinates of the triangle ABC, if A (-4, 0), B (-3, 3) and C (-1, 2), which is reflected along x-axis.
If (a, b) is reflected in the x-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 x-axis.
If (a, b) is reflected in the x-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 = -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).
Find the image coordinates 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).
Find the image coordinates of the line AB, if A (3, 2) and B (5, 2), which is reflected along y -axis.
If (a, b) is reflected in the y-axis, its image is the point (-a, b).
A (3, 2) → A’ (-3, 2)
B (5, 2) → B’ (-5, 2)
Image of the line A’ (-3, 2), B’ ( -5, 2)
Find the image coordinates of the line AB, if A (3, 2) and B (5, 2), which is reflected along y -axis.
If (a, b) is reflected in the y-axis, its image is the point (-a, b).
A (3, 2) → A’ (-3, 2)
B (5, 2) → B’ (-5, 2)
Image of the line A’ (-3, 2), B’ ( -5, 2)
Graph the reflection of the polygon in the given line: y = -3
Point A is 1 unit below the line, so its reflection is 1 unit above the line at A’ (-6, -2).
Point B is 2 units above the line, so its reflection is 2 units below the line at B’ (-5, -5).
Point C is 1 unit above the line, so its reflection is 1 unit below the line at C’ (-3, -4).
Graph the reflection of the polygon in the given line: y = -3
Point A is 1 unit below the line, so its reflection is 1 unit above the line at A’ (-6, -2).
Point B is 2 units above the line, so its reflection is 2 units below the line at B’ (-5, -5).
Point C is 1 unit above the line, so its reflection is 1 unit below the line at C’ (-3, -4).
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-axis.
Point A is 2 units to the right of the line, so its reflection is 2 units to the left of the line at A’ (-2,3).
Point B is 6 units to the right of the line, so its reflection is 6 units to the left of the line at B’ (-6,1).
Point C is 7 units to the right of the line, so its reflection is 7 units to the left of 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 y-axis.
Point A is 2 units to the right of the line, so its reflection is 2 units to the left of the line at A’ (-2,3).
Point B is 6 units to the right of the line, so its reflection is 6 units to the left of the line at B’ (-6,1).
Point C is 7 units to the right of the line, so its reflection is 7 units to the left of the line at C’ (-7, 5).
If (a, b) is reflected in the line y = -x, its image is the point ________.
If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
If (a, b) is reflected in the line y = -x, its image is the point ________.
If (a, b) is reflected in the line y = -x, its image is the point (-b, -a).
If (a, b) is reflected in the line y = x, its image is the point_________.
If (a, b) is reflected in the line y = x, its image is the point (b, a).
If (a, b) is reflected in the line y = x, its image is the point_________.
If (a, b) is reflected in the line y = x, its image is the point (b, a).
Graph the image 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).
Graph the image 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 = 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).
Find the image coordinates 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).
Find the image coordinates of the line AB, if A (2,3) and B (2,5), which is reflected along x-axis.
If (a, b) is reflected in the x-axis, its image is the point (a, -b).
A (2,3) → A’ (2, -3)
B (2,5) → B’ (2, -5)
Image of the points A’ (2, -3), B’ (2, -5)
Find the image coordinates of the line AB, if A (2,3) and B (2,5), which is reflected along x-axis.
If (a, b) is reflected in the x-axis, its image is the point (a, -b).
A (2,3) → A’ (2, -3)
B (2,5) → B’ (2, -5)
Image of the points A’ (2, -3), B’ (2, -5)
Graph the reflection of the polygon in the given line: x= -1
Point A is 5 units to the left of the line, so its reflection is 5 units to the right of the line at A’ (4, -4).
Point B is 4 units to the left of the line, so its reflection is 4 units to the right of the line at B’ (3, -1).
Point C is 2 units to the left of the line, so its reflection is 2 units to the right of the line at C’ (1, -2).
>>>Plot the points to obtain the graph.
Graph the reflection of the polygon in the given line: x= -1
Point A is 5 units to the left of the line, so its reflection is 5 units to the right of the line at A’ (4, -4).
Point B is 4 units to the left of the line, so its reflection is 4 units to the right of the line at B’ (3, -1).
Point C is 2 units to the left of the line, so its reflection is 2 units to the right of the line at C’ (1, -2).
>>>Plot the points to obtain the graph.
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 line x = 3.
The result of flipping a triangle on a line of reflection based on a coordinate system is a figure known as a triangle reflection. Therefore, it's crucial to understand the following terminology when researching and working on the reflection of polygons, such as the triangle:
Pre-image: The primary image, in this case, is a triangle, which is reflected across a line.
Image: The triangle being reflected and the result after being reflected again. To reflect a triangle, you must first reflect the three points that make up each triangle over the line of reflection and then use the algebraic reflection properties on each coordinate.
¶In a triangle reflection, the pre-point image and the image's point are at the same distance from the line of reflection. Something is one method of doing this correctly.
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 line x = 3.
The result of flipping a triangle on a line of reflection based on a coordinate system is a figure known as a triangle reflection. Therefore, it's crucial to understand the following terminology when researching and working on the reflection of polygons, such as the triangle:
Pre-image: The primary image, in this case, is a triangle, which is reflected across a line.
Image: The triangle being reflected and the result after being reflected again. To reflect a triangle, you must first reflect the three points that make up each triangle over the line of reflection and then use the algebraic reflection properties on each coordinate.
¶In a triangle reflection, the pre-point image and the image's point are at the same distance from the line of reflection. Something is one method of doing this correctly.
Graph the reflection of the polygon in the given line: x- axis.
If (a, b) is reflected in the x-axis, its image is the point (a, -b).
A (2,3) → A’ (2, -3)
B (6,1) → B’ (6, -1)
C (7,5) → C’ (7, -5)
>>>Therefore, the points of reflection of the given polygon are: (2,-3); (6,-1); (7,-5).
Graph the reflection of the polygon in the given line: x- axis.
If (a, b) is reflected in the x-axis, its image is the point (a, -b).
A (2,3) → A’ (2, -3)
B (6,1) → B’ (6, -1)
C (7,5) → C’ (7, -5)
>>>Therefore, the points of reflection of the given polygon are: (2,-3); (6,-1); (7,-5).
