5.03 Rotations
Interactive practice questions
Which shape corresponds to a rotation of triangle $R$R by $270^\circ$270° clockwise about the origin?
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 a Coordinate Plane. The y-axis ranges from $-5$−5 to $5$5. The x-axis ranges from $-5$−5 to $5$5.
In the first quadrant lies a dark blue triangle labeled $P$P and has vertices with coordinates $\left(2,1\right)$(2,1), $\left(1,5\right)$(1,5), and $\left(4,5\right)$(4,5). This triangle is overlapped by a violet triangle labeled $Q$Q which has vertices with coordinates $\left(1,2\right)$(1,2), $\left(5,1\right)$(5,1), and $\left(5,4\right)$(5,4).
In the second quadrant lies an light blue triangle labeled $W$W and has vertices with coordinates $\left(-2,1\right)$(−2,1), $\left(-1,5\right)$(−1,5), and $\left(-4,5\right)$(−4,5). This triangle is overlapped by a dark green triangle labeled $V$V which has vertices with coordinates $\left(-1,2\right)$(−1,2), $\left(-5,1\right)$(−5,1), and $\left(-5,4\right)$(−5,4).
In the third quadrant lies a red triangle labeled $T$T and has vertices with coordinates $\left(-2,-1\right)$(−2,−1), $\left(-1,-5\right)$(−1,−5), and $\left(-4,-5\right)$(−4,−5). This triangle is overlapped by a light green triangle labeled $U$U which has vertices with coordinates $\left(-1,-2\right)$(−1,−2), $\left(-5,-1\right)$(−5,−1), and $\left(-5,-4\right)$(−5,−4).
In the fourth quadrant lies a yellow triangle labeled $R$R and has vertices with coordinates $\left(1,-2\right)$(1,−2), $\left(5,-1\right)$(5,−1), and $\left(5,-4\right)$(5,−4). This triangle is overlapped by an orange triangle labeled $S$S which has has vertices with coordinates $\left(2,-1\right)$(2,−1), $\left(1,-5\right)$(1,−5), and $\left(4,-5\right)$(4,−5).
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′.