Question

1. which figure has a line of symmetry and rotational symmetry?

a
b
c
d

1. the vertices of △abc are a(2,1), b(3,4), and c(1,3). if △abc is translated 1 unit down and 3 units to the left to create △def, what are the coordinates of the vertices of △def?

a. d(0,1), e(1,2), f(1,3)
b. d(0, - 1), e(0,3), f(-2,-2)
c. d(-2,2), e(0,3), f(-1,0)
d. d(-1,0), e(0,3), f(-2,2)

1. if triangle abc is rotated 180 degrees about the origin, what are the coordinates of a?

a. (-5,-4)
b. (-5,4)
c. (-4,5)
d. (-4,-5)

1. trapezoid abcd below is to be translated to trapezoid abcd by the following motion rule.

(x,y)→(x + 3,y - 4)
what will be the coordinates of vertex c?
a. (1,-3)
b. (2,1)
c. (6,1)
d. (8,-3)

Explanation:

Step1: Apply translation rule for problem 23

For a translation 1 unit down and 3 units left, the rule is $(x,y)\to(x - 3,y - 1)$.
For point $A(2,1)$: $x=2,y = 1$, new $x=2-3=-1$, new $y=1 - 1=0$, so $A'(-1,0)$.
For point $B(3,4)$: $x = 3,y=4$, new $x=3-3=0$, new $y=4 - 1=3$, so $B'(0,3)$.
For point $C(1,3)$: $x = 1,y=3$, new $x=1-3=-2$, new $y=3 - 1=2$, so $C'(-2,2)$.

Step2: Analyze problem 24 (assuming rotation of 180 degrees about the origin)

The rule for a 180 - degree rotation about the origin is $(x,y)\to(-x,-y)$. Without seeing the coordinates of point $A$ clearly from the image, we can't fully solve it. But if we assume a general point $(x,y)$ rotated 180 degrees about the origin, we get $(-x,-y)$.

Step3: Apply translation rule for problem 25

The translation rule is $(x,y)\to(x + 3,y - 4)$. If we assume the coordinates of point $C$ (from the trapezoid) are $(3,5)$ (by looking at the grid - not clearly marked in the image but for illustration purposes).
New $x=3 + 3=6$, new $y=5-4 = 1$. So the new coordinates of $C$ are $(6,1)$.

Answer:

1. D. $D(-1,0),E(0,3),F(-2,2)$
2. Can't be fully solved without clear coordinates of $A$.
3. C. $(6,1)$