Question

test name: translation assessment
test id: 01888
date: 08/18/2023

1. which best describes the rigid - motion of rolling a marble across a table?

a. rotation
b. translation and rotation
c. translation and reflection
d. translation

1. a teacher draws an angle abc on a coordinate grid with a measure of 15°. they translate the angle 5 units to the right. which statement is true?

a. after translation, the angle abc measures 10°.
b. after translation, the angle abc measures 15°.
c. after translation, the angle abc measures 20°.
d. after translation, the angle abc measures 75°.

1. a line segment is shown on a coordinate grid.

the line segment is translated 2 units down. which image shows the result of the translation?
a.
b.
c.
d.

1. a rectangle is shown on a coordinate grid.

what are the coordinates of the vertices of the rectangle after it is translated down by 2 units?
a. a(-6,-2), b(-1,-2), c(-1,-5), d(-6,-5)
b. a(-6,-2), b(-3,-2), c(-3,-5), d(-6,-5)
c. a(-6,-4), b(-1,-4), c(-1,-7), d(-6,-7)
d. a(-6,0), b(-1,0), c(-1,-3), d(-6,-3)

1. triangle abc is shown on a coordinate grid.

if triangle abc is translated 4 units up, what are the coordinates of the vertices of abc?
a. a(-2,3), b(2,6), c(4,3)
b. a(2,-1), b(6,2), c(8,-1)
c. a(-6,-1), b(6,2), c(10,-1)
d. a(-2,-5), b(2,-4), c(4,-4)

Explanation:

Step1: Understand rigid - motion of a marble

When a marble rolls across a table, it moves from one place to another (translation) and also spins (rotation). So the rigid - motion of rolling a marble across a table is translation and rotation.

Step2: Recall properties of translation of an angle

Translation is a rigid - motion that preserves the shape and size of a figure. So, when an angle is translated, its measure does not change. If angle $ABC$ has a measure of $15^{\circ}$ and is translated 5 units to the right, it still measures $15^{\circ}$.

Step3: Apply translation rule for a line - segment

When a line - segment is translated 2 units down, the $y$ - coordinates of all its points decrease by 2.

Step4: Apply translation rule for a rectangle

When a rectangle is translated down by 2 units, the $y$ - coordinates of all its vertices decrease by 2.

Step5: Apply translation rule for a triangle

When a triangle is translated 4 units up, the $y$ - coordinates of all its vertices increase by 4.

Answer:

1. B. Translation and rotation
2. B. After translation, the angle $ABC$ measures $15^{\circ}$.
3. (No options for the image part are described in text, but conceptually, the correct one is the one with $y$ - coordinates of endpoints decreased by 2)
4. (No original coordinates given, but conceptually, subtract 2 from the $y$ - coordinates of original vertices)
5. A. $A'(-2,3),B'(2,6),C'(4,3)$ (assuming original triangle vertices have appropriate $y$ - coordinates such that adding 4 gives these new ones)