Question

lations & translations
graph the given rotation. write the coordinates of the pre - image and image.

1. rotation 180° clockwise

a(__, ) b(, __)
a’(__, ) b’(, __)

1. rotation 180° counterclockwise

x(__, ) y(, __)
x’(__, ) y’(, __)

1. rotation 270° clockwise

a(__, ) a’(, __)
b(__, ) b’(, __)
c(__, ) c’(, __)
d(__, ) d’(, __)

1. rotation 90° counterclockwise

x(__, ) x’(, __)
y(__, ) y’(, __)
z(__, ) z’(, __)

Explanation:

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1. Rotation 180° Clockwise

Step1: Identify pre-image coordinates

Read points from the graph:
$A(-4, 0)$, $B(4, -8)$

Step2: Apply 180° rotation rule

For 180° rotation (clockwise/counterclockwise), the rule is $(x,y) \to (-x,-y)$:
$A'(-(-4), -(0)) = (4, 0)$
$B'(-4, -(-8)) = (-4, 8)$

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2. Rotation 180° Counterclockwise

Step1: Identify pre-image coordinates

Read points from the graph:
$X(-6, 6)$, $Y(-2, 1)$

Step2: Apply 180° rotation rule

Use the same 180° rotation rule $(x,y) \to (-x,-y)$:
$X'(-(-6), -(6)) = (6, -6)$
$Y'(-(-2), -(1)) = (2, -1)$

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3. Rotation 270° Clockwise

Step1: Identify pre-image coordinates

Read points from the graph:
$A(-3, 7)$, $B(5, 5)$, $C(5, -5)$, $D(-3, -2)$

Step2: Apply 270° clockwise rule

The rule for 270° clockwise rotation is $(x,y) \to (y, -x)$:
$A'(7, -(-3)) = (7, 3)$
$B'(5, -5)$
$C'(-5, -5)$
$D'(-2, -(-3)) = (-2, 3)$

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4. Rotation 90° Counterclockwise

Step1: Identify pre-image coordinates

Read points from the graph:
$X(-2, -6)$, $Y(1, 0)$, $Z(2, -5)$

Step2: Apply 90° counterclockwise rule

The rule for 90° counterclockwise rotation is $(x,y) \to (-y, x)$:
$X'(-(-6), -2) = (6, -2)$
$Y'(-0, 1) = (0, 1)$
$Z'(-(-5), 2) = (5, 2)$

Answer:

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1. Rotation 180° Clockwise

$A(-4, 0)$ $B(4, -8)$
$A'(4, 0)$ $B'(-4, 8)$

1. Rotation 180° Counterclockwise

$X(-6, 6)$ $Y(-2, 1)$
$X'(6, -6)$ $Y'(2, -1)$

1. Rotation 270° Clockwise

$A(-3, 7)$ $A'(7, 3)$
$B(5, 5)$ $B'(5, -5)$
$C(5, -5)$ $C'(-5, -5)$
$D(-3, -2)$ $D'(-2, 3)$

1. Rotation 90° Counterclockwise

$X(-2, -6)$ $X'(6, -2)$
$Y(1, 0)$ $Y'(0, 1)$
$Z(2, -5)$ $Z'(5, 2)$