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## High school geometry

### Course: High school geometry>Unit 2

Lesson 3: Properties & definitions of transformations

# Defining transformations

Given a description of the effect of a certain transformation, we determine whether that transformation is a translation, a rotation, or a reflection.

## Want to join the conversation?

• Sal is starting to use the phrase "maps to itself" a lot and the verb 'map'. In other words, what does Point O maps to itself mean at ?
• Mapping a point basically means to change the coordinates. Mapping is mostly used on the coordinate plane, where points can be transformed (or mapped) to another place. Now, to answer your initial question, "Point O maps to itself" means that when it is transformed using some kind of transformation (rigid or non-rigid), it maintains its original position on the coordinate plane. Hope this helps! :)
• What's a perpendicular bisector? Did I miss something in one of the videos or is that just new math language?
• Break it into the two words:
Perpendicular means intersecting at right angles
Bisector means cutting into two equal parts (so cutting a line segment in half)
So perpendicular bisector would be a line or line segment that is perpendicular to a line segment and cuts that line segment in half
• I feel like I don't understand english anymore when I read these kind of problems xD
• What does Sal mean by 'maps to itself?'
• A point is mapped to itself if it's in the same place before and after the transformation.
• What does Sal mean by 'maps to itself?'
• "map" is a term which shows the movement of a point, If you start with (3,2) and it moves along a vector <0,5>, we would say that (3,2) maps to (3,7) along the vector <0,5>. So if something maps to itself, it would (2,2) would map to itself (2.2) if it is reflected across y=x line. That also shows it is on the line of reflection. If you have a figure and rotate around one of the points, then that point would not change, thus mapping to itself while all the other points would change with the rotation.
• What exactly is meant with 'the perpendicular bisector of segment PP'.
Any help would really be appreciated!
• bisect means cut in half, perpendicular is right angles, so it is a line or line segment which is at right angles to and divides the segment in half.
• Does anyone else love the way Sal says "perpendicular?" I love it!! XD
• Excuse me, however I do not understand this stuff at all, I guessed on the practice questions as well. Someone please help me, thanks.
• what is a perpendicular bisector and what does it mean for a point to map to itself
• To understand what a perpendicular bisector is we need to understand both words separately.

When a line (or line segment/ray) is perpendicular to some other line it means that their intersection point forms four 90-degree (right) angles. As a visual example, a plus sign (+) is two perpendicular lines crossing each other and creating those four right angles.

A bisector in geometry can mean slightly different things depending on what we're talking about. In our case, we are talking about lines. When a given line A is a "bisector" of a given line B it means that line A intersects line B at the middle point (or midpoint) of line B. This time, the angle does not matter. We just care that the intersection point of the two lines is equally far apart (equidistant) from the endpoints of line segment B. In other words, line B is split in half by line A.

If we take those two terms together ("perpendicular" and "bisector") and combine them, we get two lines that intersect each other at right angles (this is perpendicularity). Additionally, we also know that one of these line segments splits the other one perfectly in half (bisection). Again, a plus (+) or multiplication (×) sign is a great example of two line segments that are perpendicular bisectors of each other.

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As for your other question, when a point maps to itself it simply means that the transformation applied to does not change the actual location of the point. In our case, the entire point of a reflection is to take a given point A some distance x from a line and mirror it on the opposite side of that line as a new point A' that is also the same distance x from it.

For example, if point A is 5cm away from our line of reflection, point A' will also be 5cm away from that same line. Obviously, for this to be an actual reflection, we have to remember that the line of reflection we are given will be the perpendicular bisector of the line segment formed by points A and A'.

If we extend this logic, we see why points that are on the line of reflection map to themselves. Their distance to the line is 0. Therefore, the distance of the reflected point to the line will also be zero. Thus, the location of the point remains unchanged, and we say that the point maps to itself.

Hope this helps!:)