Exercises: Represent and Describe Transformations

A function $f$ takes inputs and produces exactly one output for each input. Which statement best describes how a geometric transformation is like a function?

Point $P$ has coordinates $(3, -1)$. Which of the following correctly applies the rule $T(x, y) = (x + 2, y - 4)$ to find the image of $P$?

Which of the following is NOT one of the four basic geometric transformations?

Triangle $ABC$ has vertices $A(1, 2)$, $B(4, 2)$, and $C(2, 5)$. A translation maps every point by the rule $T(x, y) = (x + 3, y - 1)$.

What are the coordinates of $A'$, the image of $A$ under $T$? Enter the $x$-coordinate.

Using the same triangle $ABC$ with $A(1, 2)$, $B(4, 2)$, $C(2, 5)$ and translation $T(x, y) = (x + 3, y - 1)$.

What is the $y$-coordinate of $C'$, the image of $C(2, 5)$ under $T$?

Triangle $PQR$ has vertices $P(2, 3)$, $Q(5, 3)$, $R(4, 6)$. It is reflected over the $y$-axis using the rule $M(x, y) = (-x, y)$.

What is the $x$-coordinate of $P'$, the image of $P(2, 3)$ after reflection over the $y$-axis?

A $90^\circ$ counterclockwise rotation about the origin follows the rule $R(x, y) = (-y, x)$. Which point is the image of $(3, 5)$ under this rotation?

A dilation centered at the origin with scale factor $3$ maps triangle $DEF$ to $D'E'F'$. Which statement is true about the distances and angles?