Topic 3 Study Guide

A(n) _______________ is a transformation about a point with a given angle measure.

• rotation

• translation

• reflection

• rigid motion

Tags

CCSS.HSG.CO.A.4

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

Reflections, translations, rotations, and glide reflections are the four types of _____________.

• rigid motion

• line of symmetry

• compositions

• preimages

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

A line that a figure is reflected across so that it maps onto itself is called a(n) ____________.

• line of symmetry

• line of reflection

• image

• glide reflection

Tags

CCSS.8.G.A.1

The composition of a reflection and a translation is called a(n) _______________.

• glide reflection

• rotation

• image

• translation

The set of points that a transformation acts on is called the ___________.

• preimage

• image

• reflection

• line of reflection

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

The result of a transformation is called the _______.

• image

• preimage

• rigid motion

• glide reflection

Does the transformation appear to be a rigid motion?

• Yes

• No

Answer explanation

Rigid motions maintain angle measure and side length so this is definitely a rigid motion!

Tags

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6

CCSS.HSG.CO.B.7

CCSS.HSG.CO.B.8

The vertices of  $\Delta$  HJK are H(-3, 2), J(-1, -3), and K(4, 3). What are the coordinates of the vertices of  $\Delta$  H'J'K' for a reflection over the y-axis?

• H'(3, 2), J'(1, -3), K'(-4, 3)

• H'(-3, -2), J'(-1, 3), K'(4, -3)

• H'(3, -2), J'(1, 3), K'(4, 3)

• None of the above

Answer explanation

A reflection over the y axis has the rule:
(x, y) -> (-x, y)
Let's apply that rule to each coordinate:
(-3, 2) -> (3, 2)
(-1, -3) -> (1, -3)
(4, 3) -> (-4, 3)

The vertices of  $\Delta$  HJK are H(-3, 2), J(-1, -3), and K(4, 3). What are the coordinates of the vertices of  $\Delta$  H'J'K' for a reflection over the x-axis?

• H'(3, 2), J'(1, -3), K'(-4, 3)

• H'(-3, -2), J'(-1, 3), K'(4, -3)

• H'(3, -2), J'(1, 3), K'(4, 3)

• None of the above

Answer explanation

A reflection over the x axis has the rule:
(x, y) -> (x, -y)
Let's apply that rule to each coordinate:
(-3, 2) -> (-3, -2)
(-1, -3) -> (-1, 3)
(4, 3) -> (4, -3)

The vertices of  $\Delta$  PQR are P(-4, 3), Q(-2, 3), and R(1, -3). What are the coordinates of the vertices of  $\Delta$  P'Q'R' for a translation of  $T_{<-3,\ 2>}$  ?

• P'(-7, 5), Q'(-5, 5), R'(-2, -1)

• P'(-1, 1), Q'(1, 1), R'(4, -6)

• P'(-1, 5),  Q'(-5, 1), R'(4, -1)

• None of the above

Answer explanation

This translation rule tells us we have to move each points to the left 3 units and up 2 units. So we subtract 3 from the x value and add 2 to the y value.
Let's apply this rule to each coordinate:
(-4, 3) -> (-4 - 3, 3 + 2) -> (-7, 5)
(-2, 3) -> (-2 - 3, 3 + 2) -> (-5, 5)
(1, -3) -> (1 - 3, -3 + 2) -> (-2, -1)

Tags

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.4

CCSS.HSG.CO.A.5

CCSS.HSG.CO.B.6