Answer:
1. (x, y) → (x + 3, y - 2)
Vertices of the image
a) (-2, - 3)
b) (-2, 3)
c) (2, 2)
2. (x, y) → (x - 3, y + 5)
Vertices of the image
a) (-3, 2)
b) (0, 2)
c) (0, 4)
d) (2, 4)
3. (x, y) → (x + 4, y)
Vertices of the image
a) (-1, -2)
b) (1, -2)
c) (3, -2)
4. (x, y) → (x + 6, y + 1)
Vertices of the image
a) (1, -1)
b) (1, -2)
c) (2, -2)
d) (2, -4)
e) (3, -1)
f) (3, -3)
g) (4, -3)
h) (1, -4)
5. (x, y) → (x, y - 4)
Vertices of the image
a) (0, -2)
b) (0, -3)
c) (2, -2)
d) (2, -4)
6. (x, y) → (x - 1, y + 4)
Vertices of the image
a) (-5, 3)
b) (-5, -1)
c) (-3, 0)
d) (-3, -1)
Explanation:
To identify each <u><em>IMAGE</em></u> you should perform the following steps:
- List the vertex points of the preimage (the original figure) as ordered pairs.
- Apply the transformation rule to every point of the preimage
- List the image of each vertex after applying each transformation, also as ordered pairs.
<u>1. (x, y) → (x + 3, y - 2)</u>
The rule means that every point of the preimage is translated three units to the right and 2 units down.
Vertices of the preimage Vertices of the image
a) (-5,2) (-5 + 3, -1 - 2) = (-2, - 3)
b) (-5, 5) (-5 + 3, 5 - 2) = (-2, 3)
c) (-1, 4) (-1 + 3, 4 - 2) = (2, 2)
<u>2. (x,y) → (x - 3, y + 5)</u>
The rule means that every point of the preimage is translated three units to the left and five units down.
Vertices of the preimage Vertices of the image
a) (0, -3) (0 - 3, -3 + 5) = (-3, 2)
b) (3, -3) (3 - 3, -3 + 5) = (0, 2)
c) (3, -1) (3 - 3, -1 + 5) = (0, 4)
d) (5, -1) (5 - 3, -1 + 5) = (2, 4)
<u>3. (x, y) → (x + 4, y)</u>
The rule represents a translation 4 units to the right.
Vertices of the preimage Vertices of the image
a) (-5, -2) (-5 + 4, -2) = (-1, -2)
b) (-3, -5) (-3 + 4, -2) = (1, -2)
c) (-1, -2) (-1 + 4, -2) = (3, -2)
<u>4. (x, y) → (x + 6, y + 1)</u>
Vertices of the preimage Vertices of the image
a) (-5, -2) (-5 + 6, -2 + 1) = (1, -1)
b) (-5, -3) (-5 + 6, -3 + 1) = (1, -2)
c) (-4, -3) (-4 + 6, -3 + 1) = (2, -2)
d) (-4, -5) (-4 + 6, -5 + 1) = (2, -4)
e) (-3, -2) (-3 + 6, -2 + 1) = (3, -1)
f) (-3, -4) (-3 + 6, -4 + 1) = (3, -3)
g) (-2, -4) (-2 + 6, -4 + 1) = (4, -3)
h) (-2, -5) (-2 + 3, -5 + 1) = (1, -4)
<u>5. (x, y) → (x, y - 4)</u>
This is a translation four units down
Vertices of the preimage Vertices of the image
a) (0, 2) (0, 2 - 4) = (0, -2)
b) (0,1) (0, 1 - 4) = (0, -3)
c) (2, 2) (2, 2 - 4) = (2, -2)
d) (2,0) (2, 0 - 4) = (2, -4)
<u>6. (x, y) → (x - 1, y + 4)</u>
This is a translation one unit to the left and four units up.
Vertices of the pre-image Vertices of the image
a) (-4, -1) (-4 - 1, -1 + 4) = (-5, 3)
b) (-4 - 5) (-4 - 1, -5 + 4) = (-5, -1)
c) (-2, -4) (- 2 - 1, -4 + 4) = (-3, 0)
d) (-2, -5) (-2 - 1, -5 + 4) = (-3, -1)