Answer :
A sequence of transformation that could be used to transform pentagon P to pentagon Q is: C. a reflection over the y-axis and then a translation seven units down.
How to perform the sequence of transformations on the pentagon?
In Mathematics and Geometry, a reflection over or across the y-axis is represented by this transformation rule (x, y) → (-x, y).
By applying a reflection over the y-axis to the coordinates of pentagon P, we have the following coordinates for its image;
(x, y) → (-x, y)
Point (1, 2) → P' (-1, 2)
Point (1, 5) → P' (-1, 5)
Next, we would apply a translation of 7 units down in order to determine the coordinates of new image (pentagon Q) as follows;
(x, y) → (x, y - 7)
P' (-1, 2) → (-1, 2 - 7) = Q (-1, -5).
P' (-1, 5) → (1, 5 - 7) = Q (1, -2).
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Complete Question:
Which sequence could be used to transform pentagon P to pentagon Q
A a 180º clockwise rotation about the origin
B a trarislation four units left and then a reflection over the x-axis
C a reflection over the y-axis and then a translation seven units down
D a translation seven units down and then a 90° clockwise rotation about the origin
Final answer:
To transform Pentagon P to Pentagon Q, perform a series of transformations: Translate, Rotate, Reflect, and Translate again.
Explanation:
To transform Pentagon P to Pentagon Q, we need to perform a series of transformations. Here is one possible sequence:
- Translate Pentagon P 3 units to the right and 2 units down to obtain a new pentagon.
- Rotate the new pentagon 90 degrees counterclockwise around its center point.
- Reflect the rotated pentagon over the y-axis.
- Translate the reflected pentagon 3 units to the left and 2 units up.
This sequence of transformations will result in Pentagon Q, which is congruent to Pentagon P.
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