Question

22 . The figure is reflected across line m and then reflected across line n. What is the resulting transformation?

A) glide reflection
B) rotation
C) reflection
D) translation



24 . The waiter places a bowl of soup in front of Abbey. In a counterclockwise direction, she passes the soup to Kai who then passes it to Haifa. Which two rotations about the center of the table describe passing the soup?
A) first 72° and then 108°
B ) first 40° and then 60°
C) first 80° and then 120°
D) first 60° and then 90°

25.  The waiter places a bowl of soup in front of Lacy. In a counterclockwise direction, she passes the soup 90°. The person receiving the soup passes it 30°. After the two passes, the soup is in front of which person?
A) Garret
B) Darcy
C) Igor
D) Haifa

28.  What are the coordinates of the vertices of the triangle under the translation (x, y) --->  (x - 1, y - 3)
A) (0, -8), (-1, -1), (-5, -4)
B)  (-8, 0), (-1, -1), (-4, -5)
C)  (5, -4), (0, 0), (5, 4)
D)  (-4, 5), (0, 0), (4, 5)

29. What is the reflection image of P(0, 0) after two reflections, first across x = -3 and then across y = 4?
A) (-8, -6)
b) (4, -3)
C) (4, -6)
D) (-6, 8)

Answer 1

`22.\\Answer:B\\\\\\24.\\\alpha=360^o:12=30^o\\\\Abbey-Kai\to2\cdot30^o=60^o\\\\Kai-Haifa\to3\cdot30^o=90^o\\\\Answer:D`



`25.\\\alpha=360^o:12=30^o\\\\Lacy+90^o\to(90^o:30^o=3)\to Igor\\\\Igor+30^o\to(30^o:30^o=1)\to Haifa\\\\Answer:D`



`28.\\(x;\ y)\to(x-1;\ y-3)\\\\\vec{a}=[-1;-3]\\\\A(-3;-2)\to A'(-3-1;-2-3)\to A'(-4;-5)\\\\B(0;\ 2)\to B'(0-1;\ 2-3)\to B'(-1;-1)\\\\C(-7;\ 3)\to C'(-7-1;\ 3-3)\to C'(-8;\ 0)\\\\Answer:B`



`29.\\P(0;\ 0)\\\\\Downarrow S_(x=-3)\\\\P'(-6;\ 0)\\\\\Downarrow S_(y=4)\\\\P''(-6;\ 8)\\\\Answer:D`

Answer 2

22) (B)

24) (D)

25) (D)

28) (B)

29) (D)

Explanation:

22) Firstly, the figure is reflected across line m and then the figure is reflected across line n.

The resultant figure is a rotated figure of original figure

(B) Rotation

24) Since there are 12 people sitting in a circle

Total circular angle = 360°

Angle between two people = 360/12 = 30°

Therefore, from Abbey to Kai there are 2 people between them. Hence, angle covered = 60°

From Kai to Haifa there are 3 people.

Angle covered = 90°

(D) is correct

25) Lacy passes the soup in 90° counterclockwise and then 30°.

Now soup is in front of Haifa.

(D) is correct

28)

Coordinates are ((0,2) -----> (x-1,y-3) = (-1,-1)

(-7,3) -------------> (x-1,y-3) = (-8,0)

(03,-2) --------> (-4,-5)

(B) is correct

Reflection of P(0,0) across x= -3, gives the point( -6,0)

And reflection across y=4, gives the point (0,8)

Together the reflected point is P(-6,8).

(D) is correct