Question

1.) x(5,2) y(2,-2) z(-4,-3) 90° clockwise rotation
2.) x(0,5) y(-3,8) z(2,-6) 1180° rotation
3.) x(1,3) y(4,-7) z(-2,3) 90° clockwise rotation
write coordinates before or after rotating about the origin.
rotations with coordinates

Explanation:

Step1: Recall 90 - degree clockwise rotation rule

For a 90 - degree clockwise rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(y, - x)$.

Step2: Apply rule to point X(5,2)

For point X with $x = 5$ and $y = 2$, after 90 - degree clockwise rotation, the new coordinates are $(2,-5)$.

Step3: Apply rule to point Y(2,-2)

For point Y with $x = 2$ and $y=-2$, after 90 - degree clockwise rotation, the new coordinates are $(-2,-2)$.

Step4: Apply rule to point Z(-4,-3)

For point Z with $x=-4$ and $y = - 3$, after 90 - degree clockwise rotation, the new coordinates are $(-3,4)$.

For 180 - degree rotation about the origin, the transformation rule for a point $(x,y)$ is $(x,y)\to(-x,-y)$.

Step5: Apply 180 - degree rotation rule to point X(0,5)

For point X with $x = 0$ and $y = 5$, after 180 - degree rotation, the new coordinates are $(0,-5)$.

Step6: Apply 180 - degree rotation rule to point Y(-3,8)

For point Y with $x=-3$ and $y = 8$, after 180 - degree rotation, the new coordinates are $(3,-8)$.

Step7: Apply 180 - degree rotation rule to point Z(2,-6)

For point Z with $x = 2$ and $y=-6$, after 180 - degree rotation, the new coordinates are $(-2,6)$.

For the second 90 - degree clockwise rotation:

Step8: Apply 90 - degree clockwise rotation rule to point X(1,3)

For point X with $x = 1$ and $y = 3$, after 90 - degree clockwise rotation, the new coordinates are $(3,-1)$.

Step9: Apply 90 - degree clockwise rotation rule to point Y(4,-7)

For point Y with $x = 4$ and $y=-7$, after 90 - degree clockwise rotation, the new coordinates are $(-7,-4)$.

Step10: Apply 90 - degree clockwise rotation rule to point Z(-2,3)

For point Z with $x=-2$ and $y = 3$, after 90 - degree clockwise rotation, the new coordinates are $(3,2)$.

Answer:

1. X(2,-5), Y(-2,-2), Z(-3,4)
2. X(0,-5), Y(3,-8), Z(-2,6)
3. X(3,-1), Y(-7,-4), Z(3,2)