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Q: What is a point of symmetry and a line containing that point?

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False

false

true

Line symmetry = Reflection symmetry. Point symmetry = Rotational symmetry.

The letters S and N have point symmetry but not line symmetry.

something that has point symmetry is shapes with thought points

True.

the distance from a point on either ray of the angle that is equidistance from the axis of symmetry is the line of symmetry. the line of symmetry dives the angle in half.

If it is a straight line then it has lateral symmetry along its length. It also has symmetry at every point along its length.

Only if it is in the form of an isosceles trapezoid

A line of symmetry or its diagonal

true

There are infinitely many such shapes. To start with, any regular will do.

If the central point of the straight line is placed exactly on the middle, and such central point has an axis, it will have a rotational symmetry.

Yes a line of symmetry creates a 'mirror image' of each side.

Line of Symmetry

coincide with

coincide with

Yes, it is symmetric about a line perpendicular to it at any point.

A line but not a point.

When a shape is rotated about its centre, if it comes to rest in a position and looks exactly like the original, then it has rotational symmetry. A shape like an equilateral triangle would therefore have an order of rotational symmetry of 3. The general rule for a regular polygon (shapes such as pentagons, heptagons, octagons etc. is, that the number of sides is the same as the number of lines of symmetry, which is also the same as the rotational symmetry order). This means that a regular hexagon has 6 sides, 6 lines of symmetry and an order of rotational symmetry of 6. Following from this, then a square, which is a regular polygon, has 4 sides, 4 lines of symmetry and an order of rotational symmetry of 4. If a shape has rotational symmetry, it must have either line symmetry or point symmetry or both. For example, a five pointed star has 5 lines of symmetry and rotational symmetry of order 5, but does not have point symmetry. A parallelogram has no line of symmetry, but has rotational symmetry of order 2 and also point symmetry. Only a shape which has line symmetry or point symmetry can have rotational symmetry. When there is point symmetry and also rotational symmetry, the order of the latter is even. For example, the letter 'S' has rotational symmetry of order 2, the regular hexagon of order 6. On this basis, we would suggest that the letter 'F' does not have a rotational symmetry order as it does not have either line symmetry or point symmetry. It doesn't have a centre around which you could rotate it. Sounds weird, but given the definitions, we think this is the case.

... point on the other side of the line at the same distance from the lien.

If the question refers to a single completely geometrically straight line of finite length in a plane, then a straight line will have two lines of symmetry. One symmetry line is perpendicular to the line being discussed and one symmetry line coincides with the line being discussed. The symmetry operation here is the one where every point of the figure is flipped perpendicularly across the symmetry line and the object is symmetric if that flipping produced exactly the same set of points. (Said differently, if flipping the set of points through a line produced an exact replica of the original set of points, then the like determining the flip is a symmetry line.) One level of complication occurs if the straight line which is the subject of the symmetry question is an infinitely long straight line. In such a case one symmetry line still coincides with the actual line, but all lines that are perpendicular to the straight line will be lines of symmetry. Thus, an infinitely long straight line has no single point as its "middle" and has an infinitely many symmetry lines consisting of all possible lines perpendicular to the original line.

The distance is 0.

true