HELP I AM BEHIND IN CLASSES
Match the transformation with the transformation rule.
Column A
1.
Translation 3 units left and 5 units up:
Translation 3 units left and 5 units up
2.
Rotation 90° clockwise
:
Rotation 90° clockwise
3.
Reflection over the x-axis:
Reflection over the x-axis
4.
Reflection over the y-axis:
Reflection over the y-axis
5.
Translation 5 units right and 3 units down:
Translation 5 units right and 3 units down
6.
Rotation 90° counter-clockwise
:
Rotation 90° counter-clockwise
7.
Rotation 180° in either direction - same as a reflection over the x and y axis
:
Rotation 180° in either direction - same as a reflection over the x and y axis
Column B
a.
(x, y) → (x - 3, y + 5)
b.(x, y) → (x , -y)
c.(x, y) → (-y, x)
d.(x, y) → (x + 5, y - 3)
e.(x, y) → (-x , -y)
f.(x, y) → (y, -x)
g.(x, y) → (-x, y)
To match the transformations in Column A with their corresponding transformation rules in Column B, we need to understand the different types of transformations and how they affect the coordinates of a point.
1. Translation 3 units left and 5 units up:
This means the point moves 3 units to the left (decreasing the x-coordinate by 3) and 5 units up (increasing the y-coordinate by 5). The corresponding transformation rule would be (x, y) → (x - 3, y + 5). So, the answer in Column B is 'a'.
2. Rotation 90° clockwise:
This means the point rotates 90° in a clockwise direction around the origin. The corresponding transformation rule would be (x, y) → (y, -x). So, the answer in Column B is 'f'.
3. Reflection over the x-axis:
This means the point is flipped over the x-axis, changing the sign of the y-coordinate. The corresponding transformation rule would be (x, y) → (x, -y). So, the answer in Column B is 'b'.
4. Reflection over the y-axis:
This means the point is flipped over the y-axis, changing the sign of the x-coordinate. The corresponding transformation rule would be (x, y) → (-x, y). So, the answer in Column B is 'g'.
5. Translation 5 units right and 3 units down:
This means the point moves 5 units to the right (increasing the x-coordinate by 5) and 3 units down (decreasing the y-coordinate by 3). The corresponding transformation rule would be (x, y) → (x + 5, y - 3). So, the answer in Column B is 'd'.
6. Rotation 90° counter-clockwise:
This means the point rotates 90° in a counter-clockwise direction around the origin. The corresponding transformation rule would be (x, y) → (-y, x). So, the answer in Column B is 'c'.
7. Rotation 180° in either direction - same as a reflection over the x and y axis:
This means the point rotates 180° in either direction around the origin, which is equivalent to reflecting the point over both the x-axis and the y-axis. The corresponding transformation rule would be (x, y) → (-x, -y). So, the answer in Column B is 'e'.
Therefore, the matching pairs are:
1. Translation 3 units left and 5 units up: (x, y) → (x - 3, y + 5) - Column B 'a'
2. Rotation 90° clockwise: (x, y) → (y, -x) - Column B 'f'
3. Reflection over the x-axis: (x, y) → (x, -y) - Column B 'b'
4. Reflection over the y-axis: (x, y) → (-x, y) - Column B 'g'
5. Translation 5 units right and 3 units down: (x, y) → (x + 5, y - 3) - Column B 'd'
6. Rotation 90° counter-clockwise: (x, y) → (-y, x) - Column B 'c'
7. Rotation 180° in either direction - same as a reflection over the x and y axis: (x, y) → (-x, -y) - Column B 'e'