Translations Lesson 9 8 Translations n n Translations

Translations n n Translations are used on the coordinate plane. A translation is a

EXAMPLE A C B D Suppose we have parallelogram ABCD as shown on the

A Notice that the entire new image Is shifted 5 units to the right

TRY THIS Translate triangle QRS 4 units to The left and 5 units up.

TRY THIS Q’ Translate triangle QRS 4 units to The left and 5 units

n n n Reflection is a mirror image of a figure. In geometry, reflectional

Symmetry n Notice that one half of the pentagon is the mirror image of

Try This n Which of the following figures have reflectional symmetry?

Try This n Which of the following figures have reflectional symmetry? YES YES NO

Symmetry n Many figures have more than one line of symmetry. Notice that the

Try This n Draw all the lines of symmetry for the following figures.

Reflections n n Reflections can also be used on the coordinate plane. A reflection

EXAMPLE A B Suppose that line segment AB is graphed as shown. If it

EXAMPLE A B Notice that the image of the line segment is a mirror

Try This Graph the image of triangle DEF after a reflection over the x-axis.

Try This Now graph the image of parallelogram ABCD after it is reflected over

Try This Line of reflection A C B D Notice that the line of

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Translations Lesson 9 -8

Translations n n Translations are used on the coordinate plane. A translation is a shift or movement of a figure a given number of places on the coordinate plane.

EXAMPLE A C B D Suppose we have parallelogram ABCD as shown on the graph. We can “translate” this shape 5 units to the right and 3 units down. The new image would look like this:

A Notice that the entire new image Is shifted 5 units to the right and 3 units down. The labels of the image are noted with a prime ‘ symbol. B A’ C B’ D C’ D’

TRY THIS Translate triangle QRS 4 units to The left and 5 units up. Q R S

TRY THIS Q’ Translate triangle QRS 4 units to The left and 5 units up. R’ Q S’ R S

Symmetry and Reflections Lesson 9 -9

n n n Reflection is a mirror image of a figure. In geometry, reflectional symmetry occurs when one half of a figure is a mirror image of the other half. The line of symmetry is the line that divides a figure into two congruent halves.

Symmetry n Notice that one half of the pentagon is the mirror image of the other. Line of symmetry

Try This n Which of the following figures have reflectional symmetry?

Try This n Which of the following figures have reflectional symmetry? YES YES NO YES

Symmetry n Many figures have more than one line of symmetry. Notice that the square has 4 lines of symmetry.

Try This n Draw all the lines of symmetry for the following figures.

Reflections n n Reflections can also be used on the coordinate plane. A reflection is a figure that has been flipped over a line of reflection.

EXAMPLE A B Suppose that line segment AB is graphed as shown. If it is reflected over the y-axis, it would look like this:

EXAMPLE A B Notice that the image of the line segment is a mirror image of the original one. It is as if the paper were folded on the y-axis and it left an identical imprint on the other side of the axis. A’ B’

Try This Graph the image of triangle DEF after a reflection over the x-axis. D E F

Try This D E F F’ E’ D’

Try This Now graph the image of parallelogram ABCD after it is reflected over x = 2 A C B D

Try This Line of reflection A C B D Notice that the line of reflection is x = 2. It is as if the paper were folded on the line x = 2. B’ A’ D’ C’