Question

1. trapezoid orst with vertices o(2, 1), r(2, 5), s(4, 5) and t(8, 1) 90° clockwise

what will be the coordinates of point n after a 270° counter - clockwise rotation about the origin?

1. what will be the coordinates of point g after a 90° counter - clockwise rotation about the origin?
2. p(8, - 2) is the image of p after a 180° rotation about the origin. what are the coordinates of p?

Explanation:

Step1: Recall 90 - degree clockwise rotation rule

For a 90 - degree clockwise rotation about the origin, the rule is $(x,y)\to(y, - x)$.
For trapezoid $QRST$ with $Q(2,1)$:
$Q'(1,-2)$
For $R(2,5)$:
$R'(5,-2)$
For $S(4,5)$:
$S'(5,-4)$
For $T(8,1)$:
$T'(1,-8)$

Step2: Recall 270 - degree counter - clockwise rotation rule

A 270 - degree counter - clockwise rotation about the origin is the same as a 90 - degree clockwise rotation. Let's assume point $N$ has coordinates $(x,y)$. After rotation, $N'(y,-x)$.

Step3: Recall 90 - degree counter - clockwise rotation rule

The rule for a 90 - degree counter - clockwise rotation about the origin is $(x,y)\to(-y,x)$. Let point $G$ have coordinates $(x,y)$, then $G'(-y,x)$.

Step4: Recall 180 - degree rotation rule

For a 180 - degree rotation about the origin, the rule is $(x,y)\to(-x,-y)$. If $P'(8,-2)$ is the image of $P$ after a 180 - degree rotation, let the coordinates of $P$ be $(x,y)$. Then $-x = 8$ and $-y=-2$. So $x=-8$ and $y = 2$, and $P(-8,2)$.

Answer:

1. $Q'(1,-2)$, $R'(5,-2)$, $S'(5,-4)$, $T'(1,-8)$
2. (No point $N$ coordinates given, can't provide specific answer but use rule $(x,y)\to(y,-x)$)
3. (No point $N$ coordinates given, can't provide specific answer but use rule $(x,y)\to(y,-x)$)
4. (No point $N$ coordinates given, can't provide specific answer but use rule $(x,y)\to(y,-x)$)
5. (No point $G$ coordinates given, can't provide specific answer but use rule $(x,y)\to(-y,x)$)
6. (No relevant information for this number)
7. $P(-8,2)$