5.03 Rotations
Interactive practice questions
Which shape corresponds to a rotation of triangle $R$R by $270^\circ$270° clockwise about the origin?
A Coordinate Plane has both the $x$x- and $y$y-axes ranging from $-5$−5 to $5$5. Both axes are marked at intervals of $1$1 unit. Eight triangles, labeled $P$P, $Q$Q, $R$R, $S$S, $T$T, $U$U, $V$V, and $W$W, of different colors are plotted on the Coordinate Plane. Two triangles overlap in each quadrant. Triangles $P$P and $Q$Q are plotted on the first quadrant. Triangle $P$P is shaded dark blue and points downward. Triangle $P$P has its vertices at $\left(2,1\right)$(2,1), $\left(1,5\right)$(1,5), and $\left(4,5\right)$(4,5). Triangle $Q$Q is shaded violet and points to the left. Triangle $Q$Q has its vertices at $\left(1,2\right)$(1,2), $\left(5,1\right)$(5,1), and $\left(5,4\right)$(5,4). Triangles $W$W and $V$V are plotted on the second quadrant. Triangle $W$W is shaded light blue and points downward. Triangle $W$W has its vertices at $\left(-2,1\right)$(−2,1), $\left(-1,5\right)$(−1,5), and $\left(-4,5\right)$(−4,5). Triangle $V$V is shaded dark green and points to the right. Triangle $V$V has its vertices at $\left(-1,2\right)$(−1,2), $\left(-5,1\right)$(−5,1), and $\left(-5,4\right)$(−5,4). Triangles $T$T and $U$U are plotted on the third quadrant. Triangle $T$T is shaded red and points upward. Triangle $T$T has its vertices at $\left(-2,-1\right)$(−2,−1), $\left(-1,-5\right)$(−1,−5), and $\left(-4,-5\right)$(−4,−5). Triangle $U$U is shaded light green and points to the right. Triangle $U$U has its vertices at $\left(-1,-2\right)$(−1,−2), $\left(-5,-1\right)$(−5,−1), and $\left(-5,-4\right)$(−5,−4). Triangles $R$R and $S$S are plotted on the fourth quadrant. Triangle $R$R is shaded yellow and points to the left. Triangle $R$R has its vertices at $\left(1,-2\right)$(1,−2), $\left(5,-1\right)$(5,−1), and $\left(5,-4\right)$(5,−4). Triangle $S$S is shaded orange and points upward. Triangle $S$S has its vertices at $\left(2,-1\right)$(2,−1), $\left(1,-5\right)$(1,−5), and $\left(4,-5\right)$(4,−5). The points and their coordinates are not explicitly given nor labeled.
Triangle $P$P
Triangle $T$T
Triangle $S$S
Triangle $W$W
Consider the following diagram.
The quadrilateral shown is rotated $90^\circ$90° clockwise about the origin.
Identify the degree of counterclockwise rotation required to transform the preimage $ABCD$ABCD into the image $A'B'C'D'$A′B′C′D′.