Geometry Unit 1: Transformations

Translations, reflections, rotations and dilations on the coordinate plane, compositions, symmetry and rigid motions. 12 questions. Have a go at each one on paper before you tap "Show me how".

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Question 1

TranslationsNo calculator

The translation $(x,y)\to(x-5,\,y+4)$ is applied to the point $(3,-2)$. Where does the point end up?

1. $(8,-6)$
2. $(-2,2)$
3. $(-2,-6)$
4. $(8,2)$

Question 2

ReflectionsNo calculator

What is the image of $(4,-1)$ after a reflection over the $y$-axis?

1. $(4,1)$
2. $(-1,4)$
3. $(-4,-1)$
4. $(-4,1)$

Question 3

ReflectionsNo calculator

Reflect the point $(2,5)$ across the line $y=x$. Where does it land?

1. $(-2,-5)$
2. $(-5,-2)$
3. $(2,-5)$
4. $(5,2)$

Question 4

RotationsNo calculator

The point $(3,1)$ is rotated $90^\circ$ counterclockwise about the origin. What is its image?

1. $(-3,-1)$
2. $(1,-3)$
3. $(3,-1)$
4. $(-1,3)$

Question 5

RotationsNo calculator

Where does $(-2,6)$ go under a rotation of $180^\circ$ about the origin?

1. $(-6,2)$
2. $(2,-6)$
3. $(-2,-6)$
4. $(6,-2)$

Question 6

DilationsNo calculator

A dilation centered at the origin with scale factor $\frac{3}{2}$ is applied to $(4,-6)$. What is the image?

1. $(6,9)$
2. $(5.5,-4.5)$
3. $\left(\frac{8}{3},-4\right)$
4. $(6,-9)$

Question 7

CompositionsNo calculator

The point $(1,4)$ is reflected over the $x$-axis and then translated 3 units left. Where does it end up?

1. $(-2,4)$
2. $(-4,1)$
3. $(4,-4)$
4. $(-2,-4)$

Question 8

SymmetryNo calculator

What is the smallest positive angle of rotation, in degrees, that maps a regular octagon onto itself?

1. $45$
2. $90$
3. $60$
4. $135$

Question 9

SymmetryNo calculator

A tile is a regular hexagon. Along how many different lines can it be folded so that the two halves match exactly?

1. $6$
2. $2$
3. $12$
4. $3$

Question 10

RotationsNo calculator

Give the point $(5,-3)$ a quarter turn clockwise around the origin. Where does it land?

1. $(-5,3)$
2. $(3,-5)$
3. $(-3,-5)$
4. $(3,5)$

Question 11

Rigid motionsNo calculator

Which of these transformations is NOT a rigid motion?

1. A translation 4 units up
2. A reflection over the line y = 1
3. A dilation with scale factor 2
4. A rotation of 90° about the origin

Question 12

TranslationsNo calculator

A translation maps $A(-1,4)$ to $A'(3,1)$. Where does the same translation map $B(2,-2)$?

1. $(6,-5)$
2. $(6,1)$
3. $(5,-6)$
4. $(-2,1)$