12 multiple-choice questions, progressively harder.
Point PPP is off mirror mmm. Which description gives its reflected image?
Solution
Correct answer: C
The fold sends P to the opposite side along the perpendicular through P. The mirror cuts that connector into equal halves. Both perpendicularity and the midpoint condition are required.
Which point is fixed by reflection across the yyy-axis?
Correct answer: A
A fixed point must lie on the mirror. Points on the y-axis have horizontal coordinate zero.
(0,−7)↦(0,−7)(0,-7)\mapsto(0,-7)(0,−7)↦(0,−7)
Reflect N(8,−3)N(8,-3)N(8,−3) across the xxx-axis. What is N′N'N′?
Correct answer: D
The horizontal mirror keeps the horizontal coordinate and reverses the height.
−(−3)=3-(-3)=3−(−3)=3
Thus N′(8,3)N'(8,3)N′(8,3).
Reflect M(−5,2)M(-5,2)M(−5,2) across the yyy-axis. What is M′M'M′?
Correct answer: B
Across the vertical axis, reverse the horizontal coordinate and keep the height.
−(−5)=5-(-5)=5−(−5)=5
The image is M′(5,2)M'(5,2)M′(5,2).
Reflect Q(9,−2)Q(9,-2)Q(9,−2) across x=4x=4x=4. What is Q′Q'Q′?
The point is five units right of the vertical mirror. Put its image five units left, keeping the same height.
x′=2(4)−9=−1x'=2(4)-9=-1x′=2(4)−9=−1
Thus Q′(−1,−2)Q'(-1,-2)Q′(−1,−2).
Reflect S(1,−8)S(1,-8)S(1,−8) across y=−3y=-3y=−3. What is S′S'S′?
The height -8 is five below the mirror at -3. The image height is five above it.
y′=2(−3)−(−8)=2y'=2(-3)-(-8)=2y′=2(−3)−(−8)=2
The horizontal coordinate stays 1.
What is the image of J(−7,3)J(-7,3)J(−7,3) across y=xy=xy=x?
The rising diagonal exchanges the coordinate roles without reversing their signs.
(−7,3)↦(3,−7)(-7,3)\mapsto(3,-7)(−7,3)↦(3,−7)
What is the image of K(6,2)K(6,2)K(6,2) across y=−xy=-xy=−x?
The falling diagonal exchanges the coordinates and reverses both signs. The new first coordinate is -2, and the new second coordinate is -6.
(6,2)↦(−2,−6)(6,2)\mapsto(-2,-6)(6,2)↦(−2,−6)
A point is 4.54.54.5 cm from its mirror. How far is it from its reflected image?
The perpendicular connector has two equal halves, one on each side of the mirror.
4.5+4.5=94.5+4.5=94.5+4.5=9
The point-to-image distance is 9 cm.
A reflection maps a segment of length 13 cm and an angle of measure 54 degrees. What are the corresponding image measurements?
A reflection preserves every distance and every angle measure. The image segment therefore remains 13 cm long, and the corresponding angle still measures 54 degrees.
The order A,B,CA,B,CA,B,C around a noncollinear triangle is counterclockwise. What is the order A′,B′,C′A',B',C'A′,B′,C′ after a reflection?
A reflection turns the marked face over. It reverses the orientation of a noncollinear triangle, so the corresponding order becomes clockwise. The point labels determine which order to compare.
A reflection exchanges the distinct endpoints UUU and VVV of a segment. Its midpoint HHH lies on the mirror. Which statement is true?
U maps to the different point V, and V maps to U, so neither is fixed. H lies on the mirror and maps to itself. The whole segment occupies the same set of positions, but that does not make its endpoints fixed.
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