Question

1. what will be the coordinates of point n after a $270^\circ$ counterclockwise rotation about the origin?

$n$(__, __)

1. what will be the coordinates of point t after a $180^\circ$ rotation about the origin?

$t$(__, __)

1. what will be the coordinates of point g after a $90^\circ$ counterclockwise rotation about the origin?

$g$(__, __)

1. what will be the coordinates of point a after a $90^\circ$ clockwise rotation about the origin?

$a$(__, __)

1. $p(8, -2)$ is the image of $p$ after a $180^\circ$ rotation about the origin. what are the coordinates of $p$?
2. $m(-5, -4)$ is the image of $m$ after a $90^\circ$ counterclockwise rotation about the origin. what are the coordinates of $m$?

Explanation:

Step1: Identify original point N

Original coordinates of $N$: $(-1, -2)$

Step2: Apply 270° CCW rotation rule

Rule: $(x,y)\to(y,-x)$
$N' = (-2, -(-1)) = (-2, 1)$

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Step1: Identify original point T

Original coordinates of $T$: $(5, 3)$

Step2: Apply 180° rotation rule

Rule: $(x,y)\to(-x,-y)$
$T' = (-5, -3)$

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Step1: Identify original point G

Original coordinates of $G$: $(-3, 4)$

Step2: Apply 90° CCW rotation rule

Rule: $(x,y)\to(-y,x)$
$G' = (-4, -3)$

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Step1: Identify original point A

Original coordinates of $A$: $(2, 1)$

Step2: Apply 90° clockwise rotation rule

Rule: $(x,y)\to(y,-x)$
$A' = (1, -2)$

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Step1: Apply 180° rotation inverse rule

Rule for inverse: $(x',y')\to(-x',-y')$
$P = (-8, -(-2)) = (-8, 2)$

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Step1: Apply 90° CCW rotation inverse rule

Inverse rule: $(x',y')\to(y',-x')$
$M = (-4, -(-5)) = (-4, 5)$

Answer:

1. $N'(-2, 1)$
2. $T'(-5, -3)$
3. $G'(-4, -3)$
4. $A'(1, -2)$
5. $P(-8, 2)$
6. $M(-4, 5)$