Exam: 02.01 Translations and Reflections

Question

Exam: 02.01 Translations and Reflections
Student Name: Abigail Antonelli

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Question 1(Multiple Choice Worth 1 points)
(02.01 MC)

A triangle has vertices at B(−3, 0), C(2, −1), D(−1, 2). Which transformation would produce an image with vertices B″(−2, 1), C″(3, 2), D″(0, −1)?

(x, y) → (x, −y) → (x + 1, y + 1)
(x, y) → (−x, y) → (x + 1, y + 1)
(x, y) → (x, −y) → (x + 2, y + 2)
(x, y) → (−x, y) → (x + 2, y + 2)
Question 2(Multiple Choice Worth 1 points)
(02.01 LC)

Trapezoid JKLM is shown on the coordinate plane below:

Trapezoid JKLM on the coordinate plane with ordered pairs at J negative 7, negative 2, at K negative 4, negative 2, at L negative 2, negative 5, at M negative 9, negative 5.

If trapezoid JKLM is translated according to the rule (x, y) → (x + 8, y − 3), what are the coordinates of point L′?

(1, −5)
(−10, 6)
(−5, 3)
(6, −8)
Question 3(Multiple Choice Worth 1 points)
(02.01 MC)

Pentagon ABCDE and pentagon A″B″C″D″E″ are shown on the coordinate plane below:

Pentagon ABCDE and pentagon A double prime B double prime C double prime D double prime E double prime on the coordinate plane with ordered pairs at A negative 5, negative 2, at B negative 7, negative 3, at C negative 6, negative 6, at D negative 3, negative 5, at E negative 3, negative 3, at A prime 3, 6, at B prime 5, 5, at C prime 4, 2, at D prime 1, 3, at E prime 1, 5.

Which two transformations are applied to pentagon ABCDE to create A″B″C″D″E″?

Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the y-axis
Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the x‒axis
Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the y-axis
Translated according to the rule (x, y) → (x + 8, y + 2) and reflected across the x‒axis
Question 4(Multiple Choice Worth 1 points)
(02.01 MC)

triangle ABC in quadrant one of the coordinate plane with side BC of length 2, triangle A prime B prime C prime in quadrant two of the coordinate plane

Triangle ABC has been reflected over the y-axis to create triangle A′B′C′. Which of the following statements is true?

B′C′ = 2
A′B′ = 2
AB = 2
AC = 2

Answer 1

Here are the answers to each of the questions based on the transformations and reflections described:

Question 1:
For the triangle with vertices B(−3, 0), C(2, −1), D(−1, 2) and needing to find the transformation to produce B″(−2, 1), C″(3, 2), D″(0, −1):

To achieve this transformation, it looks like:

1. Reflecting over the x-axis: changes the y-values' signs (A point (x, y) becomes (x, -y)).
2. Translating: shifts the points.

From examining the options:

• The option (x, y) → (−x, y) → (x + 2, y + 2) seems correct because reflecting will flip y-values, after which the translation aligns the points correctly.

Correct Answer:
(x, y) → (−x, y) → (x + 2, y + 2)

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Question 2:
For trapezoid JKLM and translating the point L(−2, −5) using the rule (x, y) → (x + 8, y − 3):

Calculating for point L′:

• L′ = (−2 + 8, −5 - 3)
• L′ = (6, -8)

Correct Answer:
(6, −8)

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Question 3:
Comparing the two pentagons ABCDE and A″B″C″D″E″, we need the transformations that yield the output.

The point transformation requires that the two transformations include a translation and a reflection.

Analyzing the choices:

• Reflecting across the y-axis will change x-values, and then you need to translate them correctly.

The transformation (x, y) → (x + 2, y + 8) and reflected across the y-axis is plausible. Each coordinate seems to increment as required.

Correct Answer:
Translated according to the rule (x, y) → (x + 2, y + 8) and reflected across the y-axis

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Question 4:
Triangle ABC with side BC of length 2, reflected over the y-axis to create triangle A′B′C′. The lengths of sides are preserved when reflecting across the y-axis.

Thus, if BC is of length 2,

• B′C′ will also be 2.

Correct Answer:
B′C′ = 2

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I hope this helps, and let me know if you have further questions!