Question

which transformation is a rigid motion?

a. (x,y)->(x+2,-1/2y)
b. (x,y)->(2x,y)
c. (x,y)->(-x,y+1)

Answer 1

A rigid motion is the action of taking an object and moving it to a different location without altering its shape or size. Reflections, rotations, translations, and glide reflections are all examples of rigid motions.

Answer 2

When we talk about transformations we assume we have a geometric figure on the plane like a triangle, and we want to move it around. But a triangle is made up of points or coordinates. So a transformation is moving each point of the triangle individually, ie transforming each point.
we could represent a translation to the right 5 units by the mapping
(x,y) -> (x + 5 , y)

Answer 3

So for example, the point (-4,1) gets transformed to what point? Lets plug (-4,1) into the mapping (x,y) -> ( x + 5, y )

(-4,1) -> (-4 + 5 , 1 ) = (1,1)

So we predict that the point (-4,1) is moved to (1,1) . And the picture confirms this.