Question

for exercises 8 and 9, polygon efgh has vertices e(4, - 3), f(2, - 4), g(1, - 1), and h(5, 0). write the coordinate notation for each rotation given. then write the coordinates of polygon efgh after each rotation.

1. clockwise rotation of 270° about the origin
2. counterclockwise rotation of 90° about the origin

Explanation:

Step1: Recall rotation rules

A clock - wise rotation of $270^{\circ}$ about the origin is equivalent to a counter - clockwise rotation of $90^{\circ}$ about the origin. The coordinate transformation rule for a counter - clockwise rotation of $90^{\circ}$ about the origin is $(x,y)\to(-y,x)$.

Step2: Apply rule to point E

For point $E(4, - 3)$, using the rule $(x,y)\to(-y,x)$, we get $E'=(3,4)$.

Step3: Apply rule to point F

For point $F(2,-4)$, using the rule $(x,y)\to(-y,x)$, we get $F'=(4,2)$.

Step4: Apply rule to point G

For point $G(1,-1)$, using the rule $(x,y)\to(-y,x)$, we get $G'=(1,1)$.

Step5: Apply rule to point H

For point $H(5,0)$, using the rule $(x,y)\to(-y,x)$, we get $H'=(0,5)$.

Step6: For counter - clockwise rotation of $90^{\circ}$ about the origin

The rule is also $(x,y)\to(-y,x)$. The results for points $E,F,G,H$ will be the same as in the clock - wise $270^{\circ}$ rotation case.

Answer:

The coordinate notation for a $270^{\circ}$ clock - wise (or $90^{\circ}$ counter - clockwise) rotation about the origin is $(x,y)\to(-y,x)$.
$E'(3,4)$, $F'(4,2)$, $G'(1,1)$, $H'(0,5)$