Question

rigid transformations: reflection, translation, rotation
read and analyze each question. use the answer sheet and shade the correct answer. do not write anything on this test paper.

1. which of the following transformations creates a figure that is congruent to the pre - image?

i. translation ii. rotation iii. dilation iv. reflection
a) iii only c) i only
b) ii only d) i, ii and iv

1. using words, describe the translation that would be made by the rule: (x,y)→(x - 5, y + 4).

a) 4 units left and 5 units up c) 5 units left and 4 units up
b) 4 units right and 5 units down d) 5 units right and 4 units down

1. which transformation is defined as a transformation along a vector such that the segment joining a point and its image has the same length as the vector and is parallel to the vector?

a) reflection c) rotation
b) translation d) dilation

1. which shadow shows a reflection of the corresponding figure?

Explanation:

Step1: Recall congruent - transformation concepts

Translation, rotation, and reflection are rigid - motions that preserve the size and shape of a figure, creating a congruent figure to the pre - image. Dilation changes the size of a figure.

Step2: Analyze the translation rule

For the rule \((x,y)\to(x - 5,y + 4)\), subtracting 5 from \(x\) moves the point 5 units to the left and adding 4 to \(y\) moves the point 4 units up.

Step3: Recall the definition of translation

Translation is a transformation along a vector such that the segment joining a point and its image has the same length as the vector and is parallel to the vector.

Step4: Recall the concept of reflection

A reflection is a transformation that flips a figure over a line of reflection. In option A, the shadow is a reflection of the figure as it is flipped over a horizontal line.

Answer:

1. D. I, II and IV
2. C. 5 units left and 4 units up
3. B. Translation
4. A.