Polygon ABCDE is the first in a pattern for a high school art project. The polygon is transformed so that the image of A' is at
(−4, 2) and the image of D' is at (−2, 1). Which transformation can be used to show that ABCDE and its image are congruent?
A. Rotate ABCDE 90° counterclockwise.
B. Translate ABCDE left 4 units and down 2 units.
C. Reflect ABCDE over the y-axis.
D. Rotate ABCDE 90° clockwise.
A. Rotate ABCDE 90° counterclockwise.
B. Translate ABCDE left 4 units and down 2 units.
C. Reflect ABCDE over the y-axis.
D. Rotate ABCDE 90° clockwise.
2 answers:
<u>ANSWER</u>
A. Rotate ABCDE 90° counterclockwise.
<u>EXPLANATION</u>
When we rotate a point through 90° counterclockwise, the mapping is
The coordinates of A are (2,4) and the coordinates of A' are (-4,2)
The coordinates of D are (1,2) and the coordinates of D' are (-2,1).
We can observe that the x and y coordinates swapped position and the first coordinate was then negated.
This is a 90° counterclockwise rotation about the origin.
Since rotation is a rigid motion the two shapes are congruent.
The correct answer is
A. Rotate ABCDE 90° counterclockwise.
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Answer: second option.
Step-by-step explanation:
You must apply
Then, given the right triangle and the angle D, the opposite side and the hypotenuse of the triangle are the following:
Therefore, when you substitute values, you have:
Reduce the fraction, then you obtain: