Question

rotations of shapes
name _______________
date ______ period__
graph the image of the figure using the transformation given.

1. rotation $180^\circ$ about the origin
2. rotation $90^\circ$ counterclockwise about the origin
3. rotation $90^\circ$ clockwise about the origin
4. rotation $180^\circ$ about the origin
5. rotation $90^\circ$ clockwise about the origin

$u(1,-2), w(0,2), k(3,2), g(3,-3)$

1. rotation $180^\circ$ about the origin

$v(2,0), s(1,3), g(5,0)$

Explanation:

Step1: Recall rotation rules

1. 180° about origin: $(x,y)\to(-x,-y)$
2. 90° counterclockwise: $(x,y)\to(-y,x)$
3. 90° clockwise: $(x,y)\to(y,-x)$

---

Problem 1: 180° about origin

First, identify vertices of $KHO$:
$K(-5,1)$, $H(-3,-2)$, $O(0,0)$

Step1: Apply 180° rotation rule

$K(-5,1)\to K'(5,-1)$
$H(-3,-2)\to H'(3,2)$
$O(0,0)\to O'(0,0)$

Step2: Plot & connect points

Graph $K'(5,-1)$, $H'(3,2)$, $O'(0,0)$ and connect.

---

Problem 2: 90° counterclockwise about origin

Identify vertices of $STL$:
$S(2,2)$, $T(4,4)$, $L(5,0)$

Step1: Apply 90° CCW rule

$S(2,2)\to S'(-2,2)$
$T(4,4)\to T'(-4,4)$
$L(5,0)\to L'(0,5)$

Step2: Plot & connect points

Graph $S'(-2,2)$, $T'(-4,4)$, $L'(0,5)$ and connect.

---

Problem 3: 90° clockwise about origin

Identify vertices of $BMFH$:
$B(-5,2)$, $M(-4,0)$, $F(-1,3)$, $H(-1,0)$

Step1: Apply 90° CW rule

$B(-5,2)\to B'(2,5)$
$M(-4,0)\to M'(0,4)$
$F(-1,3)\to F'(3,1)$
$H(-1,0)\to H'(0,1)$

Step2: Plot & connect points

Graph $B'(2,5)$, $M'(0,4)$, $F'(3,1)$, $H'(0,1)$ and connect.

---

Problem 4: 180° about origin

Identify vertices of $UHF$:
$U(-4,-2)$, $H(-2,0)$, $F(0,-2)$

Step1: Apply 180° rotation rule

$U(-4,-2)\to U'(4,2)$
$H(-2,0)\to H'(2,0)$
$F(0,-2)\to F'(0,2)$

Step2: Plot & connect points

Graph $U'(4,2)$, $H'(2,0)$, $F'(0,2)$ and connect.

---

Problem 5: 90° clockwise about origin

Given vertices: $U(1,-2)$, $W(0,2)$, $K(3,2)$, $G(3,-3)$

Step1: Apply 90° CW rule

$U(1,-2)\to U'(-2,-1)$
$W(0,2)\to W'(2,0)$
$K(3,2)\to K'(2,-3)$
$G(3,-3)\to G'(-3,-3)$

Step2: Plot & connect points

Graph $U'(-2,-1)$, $W'(2,0)$, $K'(2,-3)$, $G'(-3,-3)$ and connect.

---

Problem 6: 180° about origin

Given vertices: $V(2,0)$, $S(1,3)$, $G(5,0)$

Step1: Apply 180° rotation rule

$V(2,0)\to V'(-2,0)$
$S(1,3)\to S'(-1,-3)$
$G(5,0)\to G'(-5,0)$

Step2: Plot & connect points

Graph $V'(-2,0)$, $S'(-1,-3)$, $G'(-5,0)$ and connect.

Answer:

1. Transformed vertices: $K'(5,-1)$, $H'(3,2)$, $O'(0,0)$ (plot and connect these points)
2. Transformed vertices: $S'(-2,2)$, $T'(-4,4)$, $L'(0,5)$ (plot and connect these points)
3. Transformed vertices: $B'(2,5)$, $M'(0,4)$, $F'(3,1)$, $H'(0,1)$ (plot and connect these points)
4. Transformed vertices: $U'(4,2)$, $H'(2,0)$, $F'(0,2)$ (plot and connect these points)
5. Transformed vertices: $U'(-2,-1)$, $W'(2,0)$, $K'(2,-3)$, $G'(-3,-3)$ (plot and connect these points)
6. Transformed vertices: $V'(-2,0)$, $S'(-1,-3)$, $G'(-5,0)$ (plot and connect these points)