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 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:

                     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.
>>>when, a point is reflected with respect to the line then, the coordinates becomes twice the distance between the line and the point from the real point because we have to cover the distance on both sides.
>>>Hence, the reflection of (2,3) with respect to x=3 becomes
x-coordinate: 2+2(3-2) = 4; y-coordinate: y=3.
>>>Similarly, the reflection of (6,1) with respect to x=3 becomes:
x-coordinate: 6-2(6-3) =0 ; y-coordinate: y=1
>>>Similarly, the reflection of (7,5) with respect to x=3 becomes:
x-coordinate: 7-2(7-3) =-1 ; y-coordinate: y=5.
>>>Therefore, the required points of reflection are:(4,3);(0,1);(-1,5).
Required graph is:

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.