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Translations: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

One translation sends $A(-3,4)$ to $A'(2,-2)$ and $B(t,1)$ to $B'(8,-5)$ . Find $t$ .

Answer choices for question 1 A $13$ B $6$ C $-3$ D $3$
2

A proposed translation maps $A(1,1)$ to $A'(4,-1)$ , $B(-2,0)$ to $B'(1,-2)$ , and $C(0,3)$ to $C'(3,2)$ . Which statement is correct?

Answer choices for question 2 A All three pairs have displacement $(3,-2)$ . B Only the first two pairs have the same displacement. C Only the first and third pairs agree. D No two pairs have the same displacement.
3

A translation sends $A(-4,6)$ to itself. What must it do to $B(5,-2)$ ?

Answer choices for question 3 A Send $B$ to $B'(1,4)$ . B Send $B$ to $B'(-4,6)$ . C Send $B$ to $B'(5,-2)$ . D Send $B$ to $B'(-5,2)$ .
4

A translation pairs angles whose measures are $3p+4$ degrees and $5p-18$ degrees. Find their common measure.

Answer choices for question 4 A $37^\circ$ B $11^\circ$ C $22^\circ$ D $55^\circ$
5

An unknown transformation agrees with one translation at three tested points. Is that enough to prove the unknown rule is that translation at every point in the plane?

Answer choices for question 5 A Yes, any three matching points prove a rule for the whole plane. B Yes, because every transformation is a translation. C No, the rule could act differently at an untested point. D No, because three points can never fit one translation.
6

Point $P$ lies between $A$ and $B$ , with $AP=4$ cm and $PB=9$ cm. A translation maps them to $A',P',B'$ . Which pair gives $A'P'$ and $A'B'$ ?

Answer choices for question 6 A $9$ cm and $13$ cm B $4$ cm and $5$ cm C $13$ cm and $13$ cm D $4$ cm and $13$ cm
7

A translation has displacement $(-6,2)$ . The image of $B(s,s-9)$ is $B'(0,-1)$ . What is the preimage point $B$ ?

Answer choices for question 7 A $B(-6,-7)$ B $B(6,-3)$ C $B(6,3)$ D $B(0,-1)$
8

In the specified correspondence, $A(0,0)\mapsto A'(0,0)$ and $B(2,0)\mapsto B'(0,2)$ . Both segments have length 2. Can a translation make these matches?

Answer choices for question 8 A No, because the two point displacements differ. B Yes, because the segment lengths agree. C Yes, because both segments have an endpoint at the origin. D No, because translations cannot move points on an axis.
9

A rule moves every point eight units right and six units down. Which statement about its displacement is justified here?

Answer choices for question 9 A The straight travel distance must be 14 units. B The horizontal and vertical changes are 8 and -6; adding 8 and 6 does not give the straight travel distance. C The travel distance is different for each starting point. D The displacement pair is $(6,-8)$ .
10

A translation has rule $(x,y)\mapsto(x+3,y)$ . What is the image of the entire line $y=2$ ?

Answer choices for question 10 A The line $y=5$ . B The single point $(3,2)$ . C The same line $y=2$ . D The line $x=5$ .
11

A translation sends $A(-1,2)$ to $A'(4,-2)$ . Segments $AB$ and $CD$ are parallel. Which conclusion is guaranteed without knowing the other coordinates?

Answer choices for question 11 A $A'B'\parallel C'D'$ . B $A'B'\perp C'D'$ . C $A'B'=C'D'$ . D $B'=A'$ .
12

A translation sends $A(u,1)$ to $A'(7,4)$ and $B(-2,v)$ to $B'(3,1)$ . Which displacement and missing values fit both pairs?

Answer choices for question 12 A Displacement $(-5,-3)$ ; $u=12$ , $v=4$ . B Displacement $(5,3)$ ; $u=12$ , $v=4$ . C Displacement $(3,5)$ ; $u=4$ , $v=-4$ . D Displacement $(5,3)$ ; $u=2$ , $v=-2$ .

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