Slide
Can you help Marco reset the monuments as you play around with Rigid Geometric Transformations?
Learn
We explored transformations in Phaseville!
Click here to review
Reflections
A reflection about a line m maps every point P to a point P' such that if P is not on m, then m is the perpendicular bisector of PP' and if P is on m, then P=P'
To reflect, we only need a line to reflect over. The distance from each point to the line of reflection is the same as the distance from the reflected point to the line of reflection.​
​In the activity below, move the black points to change the triangle or the line of reflection to see what happens when ΔABC is reflected over your line.
©MathBait® created with GeoGebra
Challenge
Can you get move Dino through this reflection maze? Click on Dino at the start, then select the reflection tool and the line you want to reflect him over. Keep going! Reflect, reflect, reflect to transport Dino to the Finish!
©MathBait® created with GeoGebra
Translations
A translation by a vector v maps every point P to its image P' such that PP'= |v | , PP' || v, and the directed segment PP' travels in the same direction as v.
All transformations are combinations of reflections! To translate, or slide, we can reflect two times.
​
Translations require vectors. A vector has magnitude and direction. This tells us how far to go and which way to go.
​In the activity below, move the black points to change the triangle or the vector length or direction to see what happens when ΔABC is translated by your vector.
©MathBait® created with GeoGebra
Rotations
A rotation about a point C by an angle θ maps a point P to P' such that m∠PCP'=θ and CP=CP'. If P=C, then P'=C.
A rotation is also two reflections! To rotate, we need a point to rotate about and an angle.
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In a rotation, the angle between your original point, P, your point of rotation, C, and your rotated point, P', must be equal to your angle of rotation, θ.
​In the activity below, move the black points to change the triangle, the center of rotation, or the angle to see what happens when ΔABC is rotated. Remember! Clockwise gives us a negative angle measure and counter-clockwise gives us a positive angle measure.
©MathBait® created with GeoGebra
Play
Follow along in The Shape of Everything or try to reset the monuments on your own!
Hint: Try moving Monument 6 first to avoid the Simultaneous Somersault
©MathBait®
Sample Digital Game Created with GeoGebra
