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5.03 Rotations

Adaptive
Worksheet

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

A

Triangle $T$T

B

Triangle $S$S

C

Triangle $W$W

D
Easy
< 1min

Consider the following diagram.

Easy
< 1min

The quadrilateral shown is rotated $90^\circ$90° clockwise about the origin.

Medium
< 1min

Identify the degree of counterclockwise rotation required to transform the preimage $ABCD$ABCD into the image $A'B'C'D'$ABCD.

Medium
< 1min
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Outcomes

G.RLT.3

The student will solve problems, including contextual problems, involving symmetry and transformation.

G.RLT.3cii

Given an image or preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include: ii) reflections over any horizontal or vertical line or the lines y = x or y = -x;

G.RLT.3ciii

Given an image or preimage, identify the transformation or combination of transformations that has/have occurred. Transformations include: iii) clockwise or counterclockwise rotations of 90°, 180°, 270°, or 360° on a coordinate grid where the center of rotation is limited to the origin;

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