12 multiple-choice questions, progressively harder.
Which instruction defines a translation of a figure?
Solution
Correct answer: C
A translation is one common slide. Its instruction applies to every point, including points along sides and inside a region. Different distances or directions would violate that definition.
Under a translation, K↦K′K\mapsto K'K↦K′. Which statement identifies the preimage and image correctly?
Correct answer: A
The arrow in K↦K′K\mapsto K'K↦K′ runs from the starting point to its assigned destination. Thus K is the preimage point and K-prime is the image point. The prime is part of the image's name, not a measurement.
Translate B(−2,5)B(-2,5)B(−2,5) four units right and three units down. What is B′B'B′?
Correct answer: B
Right four adds 4 to the horizontal coordinate.
x′=−2+4=2x'=-2+4=2x′=−2+4=2
Down three subtracts 3 from the vertical coordinate.
y′=5−3=2y'=5-3=2y′=5−3=2
The image is B′(2,2)B'(2,2)B′(2,2).
What does displacement pair (−5,2)(-5,2)(−5,2) tell each point to do?
Correct answer: D
The first entry is the horizontal change: negative five means left five. The second is the vertical change: positive two means up two. Add these changes to each starting point.
One point travels 6 cm left and another travels 6 cm right. Can those two journeys belong to one translation?
Equal travel distance is only one requirement. A translation also gives every point the same direction. Left and right are opposite directions, so these journeys cannot come from one translation.
A translation has rule (x,y)↦(x,y−7)(x,y)\mapsto(x,y-7)(x,y)↦(x,y−7). Which coordinate stays unchanged?
The image's first coordinate is the original x with no addition. The second coordinate decreases by 7.
(x,y)↦(x,y−7)(x,y)\mapsto(x,y-7)(x,y)↦(x,y−7)
Every point moves straight down, and its horizontal coordinate stays unchanged.
Segment MNMNMN is 9 cm long. A translation moves every point 3 cm. How long is M′N′M'N'M′N′?
A translation preserves the distance between M and N, so the corresponding segment keeps its length.
M′N′=9 cmM'N'=9\text{ cm}M′N′=9 cm
The 3 cm describes travel, not a change in side length.
A translation maps A,B,CA,B,CA,B,C to A′,B′,C′A',B',C'A′,B′,C′ respectively. If m∠ABC=83∘m\angle ABC=83^\circm∠ABC=83∘, what is m∠A′B′C′m\angle A'B'C'm∠A′B′C′?
The two rays forming the angle slide together. Angle measure is preserved, so
m∠A′B′C′=83∘.m\angle A'B'C'=83^\circ.m∠A′B′C′=83∘.
A translation sends M(3,−4)M(3,-4)M(3,−4) to M′(−1,2)M'(-1,2)M′(−1,2). What is its displacement pair?
Subtract each starting coordinate from the matching image coordinate.
−1−3=−4-1-3=-4−1−3=−4
2−(−4)=62-(-4)=62−(−4)=6
The displacement is (−4,6)(-4,6)(−4,6), four left and six up.
What does the zero translation do?
The zero translation has displacement (0,0)(0,0)(0,0). Neither coordinate changes.
(x,y)↦(x,y)(x,y)\mapsto(x,y)(x,y)↦(x,y)
Every point is its own image.
The arrow shows A(−1,1)↦A′(2,3)A(-1,1)\mapsto A'(2,3)A(−1,1)↦A′(2,3). What displacement pair does it specify?
Use image minus starting coordinate in each direction.
2−(−1)=32-(-1)=32−(−1)=3
3−1=23-1=23−1=2
The pair is (3,2)(3,2)(3,2).
Two distinct lines are parallel. What is guaranteed about their images under one translation?
Both lines keep their directions and the separation between them under the same slide. Since their original directions agree and their separation is nonzero, their images are distinct and parallel.
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