Geometric transformations flashcards

Question 1

What is a translation in the coordinate plane?

Accepted Answer

A transformation that slides every point the same distance and direction: $(x,y)	o(x+a,\,y+b)$ where $\langle a,bangle$ is the translation vector.

Question 2

Rotate $R(2,-3)$ about the origin by $180^\circ$.

Accepted Answer

$(x,y)	o(-x,-y)$, so $R'(-2,3)$.

Question 3

What is a composition of transformations, and how is it applied?

Accepted Answer

A composition applies two or more transformations in sequence; the output of one becomes the input of the next (order matters). Example: apply $T_1$ then $T_2$ gives $T_2\circ T_1$.

Geometric transformations flashcards

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