Translations, Reflections and Rotations: Grade 8 Math Quiz – PDF Download
Ten multiple-choice questions check translations, reflections and rotations on the coordinate plane and the properties of rigid motions for standards 8.G.A.1 and 8.G.A.3. Rotations are counterclockwise about the origin. Pick one answer each, then read the explanations.
Grade 8Common Core: 8.G.A.1 · 8.G.A.3
🎯 Translations, Reflections and Rotations – Grade 8 math quiz
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Question 1
What is the image of \((2,-3)\) under the translation \((x,y)\to(x-4,\,y+5)\)?
A\((6,-8)\)
B\((-2,2)\)
C\((-2,-8)\)
D\((6,2)\)
Question 2
What is the image of \((-5,3)\) after a reflection across the \(x\)-axis?
A\((5,3)\)
B\((5,-3)\)
C\((-5,-3)\)
D\((3,-5)\)
Question 3
What is the image of \((4,1)\) after a \(90^{\circ}\) counterclockwise rotation about the origin?
A\((1,-4)\)
B\((-4,-1)\)
C\((-1,4)\)
D\((-4,1)\)
Question 4
Which single motion maps triangle \(ABC\) onto triangle \(A^{\prime}B^{\prime}C^{\prime}\)?Triangle \(ABC\) and its image.
AReflection across the x-axis
BReflection across the y-axis
CRotation of 180 degrees about the origin
DTranslation 5 units left
Question 5
Which measures stay the same when a figure is rotated about the origin?
AOnly side lengths
BSide lengths and angle measures
COnly angle measures
DNeither side lengths nor angle measures
Question 6
The figure shows a translation. Which rule describes it?A segment with endpoint \(A(-3,2)\) and its image with endpoint \(A^{\prime}(2,-1)\).
A\((x,y)\to(x+5,\,y+3)\)
B\((x,y)\to(x-5,\,y-3)\)
C\((x,y)\to(x+3,\,y-5)\)
D\((x,y)\to(x+5,\,y-3)\)
Question 7
Which rule describes a rotation of \(180^{\circ}\) about the origin?
A\((x,y)\to(-y,x)\)
B\((x,y)\to(y,-x)\)
C\((x,y)\to(-x,-y)\)
D\((x,y)\to(-x,y)\)
Question 8
Triangle \(A^{\prime}B^{\prime}C^{\prime}\) is a counterclockwise rotation of triangle \(ABC\) about the origin. What is the angle of rotation?Triangle \(ABC\) and its image.
A\(180^{\circ}\)
B\(270^{\circ}\)
C\(45^{\circ}\)
D\(90^{\circ}\)
Question 9
Two parallel lines are reflected across the \(x\)-axis. What is true about their images?
AThey are parallel.
BThey are perpendicular.
CThey cross at the origin.
DThey are no longer parallel.
Question 10
A triangle has a side of 9 cm and an angle of \(45^{\circ}\). It is rotated \(270^{\circ}\) about the origin. What are the side and angle of the image?
A\(9\text{ cm and }45^{\circ}\)
B\(9\text{ cm and }315^{\circ}\)
C\(18\text{ cm and }45^{\circ}\)
D\(9\text{ cm and }135^{\circ}\)
🎉 Quiz complete!
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Remember:
Rigid motions keep segment lengths, angle measures and parallel lines, so the image is congruent to the pre-image.
Translation: (x, y) becomes (x + a, y + b).
Reflection across the x-axis: (x, -y). Across the y-axis: (-x, y).
Rotation about the origin, counterclockwise: 90 degrees (-y, x), 180 degrees (-x, -y), 270 degrees (y, -x).
