Question

1. multi - step the coordinates of the vertices of rectangle abcd are a(-4,1), b(1,1), c(1, - 2), and d(-4,-2). find the coordinates for the image of rectangle abcd after the translation (x,y)→(x + 3,y - 2). draw the pre - image and the image.
2. travel write a rule for the translation that maps the descent of the hot air balloon.

which transformation is suggested by each of the following?

1. mountain range and its image on a lake
2. straight line path of a band marching down a street
3. wings of a butterfly

given points f(3,5), g(-1,4), and h(5,0), draw △fgh and its reflection across each of the following lines.

1. the x - axis 17. the y - axis
2. find the vertices of one of the triangles on the graph. then use arrow notation to write a rule for translating the other three triangles.

a transformation maps a onto b and c onto d.

1. name the image of a. 20. name the pre - image of b.
2. name the image of c. 22. name the pre - image of d.

Explanation:

Step1: Apply translation rule to point A

For point $A(-4,1)$, using the translation $(x,y)\to(x + 3,y - 2)$. Substitute $x=-4$ and $y = 1$: $x'=-4 + 3=-1$, $y'=1-2=-1$. So $A'(-1,-1)$.

Step2: Apply translation rule to point B

For point $B(1,1)$, substitute $x = 1$ and $y=1$ into the translation: $x'=1 + 3=4$, $y'=1-2=-1$. So $B'(4,-1)$.

Step3: Apply translation rule to point C

For point $C(1,-2)$, substitute $x = 1$ and $y=-2$: $x'=1+3 = 4$, $y'=-2-2=-4$. So $C'(4,-4)$.

Step4: Apply translation rule to point D

For point $D(-4,-2)$, substitute $x=-4$ and $y=-2$: $x'=-4 + 3=-1$, $y'=-2-2=-4$. So $D'(-1,-4)$.

Answer:

The vertices of the image of rectangle $ABCD$ are $A'(-1,-1)$, $B'(4,-1)$, $C'(4,-4)$, $D'(-1,-4)$.