Question

rotations

1. $r_{(90^{circ},0)}\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$
2. $r_{(180^{circ},0)}\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$
3. $r_{(270^{circ},0)}\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$
4. $r_{(- 90^{circ},0)}\triangle abc$, where $a(3,0)$, $b(5,3)$, and $c(7,6)$

Explanation:

Step1: Recall 90 - degree rotation rule

For a 90 - degree counter - clockwise rotation about the origin $(x,y)\to(-y,x)$.
For point A(3,0):
$x = 3,y = 0$, new coordinates are $(0,3)$.
For point B(5,3):
$x = 5,y = 3$, new coordinates are $(-3,5)$.
For point C(7,6):
$x = 7,y = 6$, new coordinates are $(-6,7)$.

Step2: Recall 180 - degree rotation rule

For a 180 - degree rotation about the origin $(x,y)\to(-x,-y)$.
For point A(3,0):
$x = 3,y = 0$, new coordinates are $(-3,0)$.
For point B(5,3):
$x = 5,y = 3$, new coordinates are $(-5,-3)$.
For point C(7,6):
$x = 7,y = 6$, new coordinates are $(-7,-6)$.

Step3: Recall 270 - degree rotation rule

For a 270 - degree counter - clockwise rotation about the origin $(x,y)\to(y,-x)$.
For point A(3,0):
$x = 3,y = 0$, new coordinates are $(0, - 3)$.
For point B(5,3):
$x = 5,y = 3$, new coordinates are $(3,-5)$.
For point C(7,6):
$x = 7,y = 6$, new coordinates are $(6,-7)$.

Step4: Recall - 90 - degree rotation rule

A - 90 - degree rotation (or 270 - degree clockwise rotation) about the origin is the same as a 270 - degree counter - clockwise rotation, $(x,y)\to(y,-x)$.
For point A(3,0):
$x = 3,y = 0$, new coordinates are $(0,-3)$.
For point B(5,3):
$x = 5,y = 3$, new coordinates are $(3,-5)$.
For point C(7,6):
$x = 7,y = 6$, new coordinates are $(6,-7)$.

Answer:

1. A'(0,3), B'(-3,5), C'(-6,7)
2. A'(-3,0), B'(-5,-3), C'(-7,-6)
3. A'(0,-3), B'(3,-5), C'(6,-7)
4. A'(0,-3), B'(3,-5), C'(6,-7)