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Reflections: Practice

12 multiple-choice questions, progressively harder.

Level 3 · Challenge 0 / 12 answered

Question 1 of 12

1

Reflection across $y=x$ sends $P(2t-1,8)$ to $P'(8,5)$ . Find $t$ .

Answer choices for question 1 A $2$ B $\frac{7}{2}$ C $5$ D $3$
2

Can reflection across $x=2$ make both matches $A(-1,4)\mapsto A'(5,4)$ and $B(7,-3)\mapsto B'(-3,-3)$ ?

Answer choices for question 2 A No; different points must travel the same distance. B Yes; both connectors are horizontal with midpoint on $x=2$ . C No; one pair is above the x-axis and the other is below. D Yes; equal heights alone are sufficient.
3

The points $P(-3,1)$ and $Q(3,5)$ are equally far from the $y$ -axis on opposite sides. Is $Q$ the reflection of $P$ across that axis?

Answer choices for question 3 A Yes; equal distances from the mirror are sufficient. B Yes; both points have positive heights. C No; their connector is not perpendicular to the mirror. D No; a reflection must change both coordinates.
4

A proposed reflection sends $A(1,2)$ to $A'(5,2)$ and $B(2,4)$ to $B'(4,5)$ . Which statement decides whether one reflection can do both?

Answer choices for question 4 A No; the first pair forces $x=3$ , which cannot change B’s height. B Yes; both first coordinates increase. C Yes; the first pair alone guarantees every other pair. D No; reflections cannot send two points to different heights.
5

Triangle $ABC$ has $A(-2,1)$ , $B(3,1)$ , and $C(0,4)$ . Reflect it across $y=-x$ . Which side corresponds to $AB$ , and what is its length?

Answer choices for question 5 A $A'C'$ from $(-1,2)$ to $(-4,0)$ ; length $5$ B $A'B'$ from $(1,-2)$ to $(1,3)$ ; length $5$ C $A'B'$ from $(-1,2)$ to $(-1,-3)$ ; length $5$ D $A'B'$ from $(-1,2)$ to $(-1,-3)$ ; length $10$
6

For what value of $t$ is $P(t,3t-8)$ fixed by reflection across $y=x$ ?

Answer choices for question 6 A $4$ B $-4$ C $8$ D $2$
7

Reflection across $y=-2$ sends the entire horizontal line $y=5$ to which line, and does it fix any point of $y=5$ ?

Answer choices for question 7 A $y=9$ ; no point is fixed B $y=-9$ ; every point is fixed C $y=5$ ; every point is fixed D $y=-9$ ; no point of the starting line is fixed
8

A line passes through the midpoint of a nonzero point-image connector, but meets it at a 60-degree angle. Can it be the mirror for that pair?

Answer choices for question 8 A Yes; the midpoint condition is enough. B No; it must also be perpendicular to the connector. C Yes; every angle less than 90 degrees works. D No; no reflection can exchange endpoints of a segment.
9

A reflection in a vertical line sends $P(11,-4)$ to $P'(-5,-4)$ . What image does it give $Q(-2,9)$ ?

Answer choices for question 9 A $Q'(8,9)$ B $Q'(2,9)$ C $Q'(-2,-9)$ D $Q'(4,9)$
10

Distinct points $A$ and $B$ are fixed by a reflection. Point $C$ is not on line $AB$ . Which mirror and image behavior are forced?

Answer choices for question 10 A The mirror is any line through A, and C stays fixed. B The mirror is perpendicular to AB at A, and B moves. C The mirror is line AB, and C moves to the opposite side. D The mirror is line AB, and C must also stay fixed.
11

A reflection maps one angle of measure $(6n+5)^\circ$ to its corresponding angle of measure $(4n+29)^\circ$ . Find their common measure.

Answer choices for question 11 A $12^\circ$ B $77^\circ$ C $53^\circ$ D $103^\circ$
12

You have drawn the perpendicular from an off-mirror point $V$ to an oblique mirror, meeting it at $H$ . Which next step places the image of $V$ correctly?

Answer choices for question 12 A Keep V-prime on the same ray from H toward V. B Draw a line through V parallel to the mirror. C Choose any point the same distance from V as H is. D Extend VH beyond H and copy length HV onto that opposite ray.

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