Question

1. how many degrees was the figure rotated? 8. reflect the point (2, -4) over the y - axis. a (2, 4) b (-2, 4) c (-4, 2) d (-2, -4) 9. rotate the point (-3,-4) around the origin 180 degrees. state the image of the point. a (-4,-3) b (3,4) c (-4,3) d (4,-3) 10. point a is rotated 180 degrees and then flipped over the y - axis. what is a\ if a is (2,7) a (2, -7) b (-2, -7) c (2,7) d (-2, 7) 11. describe the transformations that map abc onto a\b\c\ a translate 5 up and 1 left then reflect over y b reflect over x then rotate 90 clockwise c translate 5 down and 1 left, then reflect over y d reflect over y=x then translate left 8

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation of a point $(x,y)$ about the origin, the new point is $(-y,x)$. For a 90 - degree clockwise rotation, the new point is $(y, - x)$. For a 180 - degree rotation about the origin, the new point is $(-x,-y)$. For reflection over the y - axis, the rule is $(x,y)\to(-x,y)$.

Step2: Solve question 7

By observing the figure, we can see that the figure is rotated 90 degrees counter - clockwise.

Step3: Solve question 8

Using the reflection over the y - axis rule $(x,y)\to(-x,y)$ for the point $(2,-4)$, we get $(-2,-4)$. So the answer is D.

Step4: Solve question 9

Using the 180 - degree rotation rule $(x,y)\to(-x,-y)$ for the point $(-3,-4)$, we have $-(-3)=3$ and $-(-4)=4$. So the image is $(3,4)$, and the answer is B.

Step5: Solve question 10

First, rotating point $A(2,7)$ 180 degrees gives $(-2,-7)$. Then reflecting $(-2,-7)$ over the y - axis gives $(2,-7)$. So the answer is A.

Step6: Solve question 11

By observing the triangles, we can see that the transformation is to translate 5 down and 1 left, then reflect over y. So the answer is C.

Answer:

1. A. 90 degrees counterclockwise
2. D. (-2, -4)
3. B. (3,4)
4. A. (2, -7)
5. C. translate 5 down and 1 left, then reflect over y