symetric line: Is the line in the picture is line of Symmetry of Rectangle?

[shahar]

Is the line in the picture is line of Symmetry of Rectangle?
The answer of the discussion on it is no.
Why?
(Or I am wrong and the answer is yes...; Still I ask: why?)

 

[Dr.Peterson]

Is the line in the picture is line of Symmetry of Rectangle?
The answer of the discussion on it is no.
Why?
(Or I am wrong and the answer is yes...; Still I ask: why?)

The answer is no.

Reflect any point of the square over the line, and you will find that the image is not on the square. For a line of symmetry, the result of reflection would be identical to the original.

Here is a picture of the original square (red) and its reflection (green):



A diagonal of the square would be a line of symmetry.

 

[shahar]

The answer is no.

Reflect any point of the square over the line, and you will find that the image is not on the square. For a line of symmetry, the result of reflection would be identical to the original.

Here is a picture of the original square (red) and its reflection (green):

View attachment 10422

A diagonal of the square would be a line of symmetry.

Sorry, but I can't understand the pictures. Can you formulate it again with more picture and more word.
1. Why the green rectangle is reflection?
2. Why the diagonal square of the square is the line of symmetry?
3. If I elaborate the term square to the term rectangle - Is the answer will be same? (because the picture is from the original problem and the word is rectangle - that include the word square by definition)

 

[Dr.Peterson]

Sorry, but I can't understand the pictures. Can you formulate it again with more picture and more word.
1. Why the green rectangle is reflection?
2. Why the diagonal square of the square is the line of symmetry?
3. If I elaborate the term square to the term rectangle - Is the answer will be same? (because the picture is from the original problem and the word is rectangle - that include the word square by definition)

Do you know what a reflection is?

A point is reflected across a line by locating a point the same distance on the other side of the line, in a direction perpendicular to the line. Here is a picture showing each vertex of the given square with an arrow to its reflection:



Please tell us what you know about symmetry, so we can have some idea what knowledge we can assume.

If the problem said "rectangle", so that you have to guess that it is actually a square from the way the picture looks, then you just have all the more reason to say no; a non-square rectangle has only two lines of symmetry, which are parallel to its sides.

To see that a diagonal of a square (but not of other rectangles) is a line of symmetry, just try making the same kind of drawing.