In the diagram above, In the diagram above, corresponding points on the corresponding points on the two figures are related. two figures are related. Suppose Suppose PP is any point on the is any point on the originaloriginal figure and figure and P’P’ is the is the corresponding point on the corresponding point on the imageimage figure. figure.

We say: P maps onto P’ We say: P maps onto P’ We write: P P’ We write: P P’

We often use a coordinate grid when we work with We often use a coordinate grid when we work with transformations. We use a transformations. We use a mapping rulemapping rule to describe to describe how points and their images are related. how points and their images are related.

A A mapping rulemapping rule tells you what to do to the coordinates tells you what to do to the coordinates of any point on the figure to determine the of any point on the figure to determine the coordinates of tits image.coordinates of tits image.

Example of Mapping rule:Example of Mapping rule:

(x, y) (x + 5, y - 2)(x, y) (x + 5, y - 2)

It tells you to add 5 to the x-coordinate and to subtract 2 from the It tells you to add 5 to the x-coordinate and to subtract 2 from the y-coordinate.y-coordinate.

Reflections in the lineReflections in the lineReflections in theReflections in the

YOU NEED TO MEMORIZE THESE RULES!!!YOU NEED TO MEMORIZE THESE RULES!!!

The image is congruent to the The image is congruent to the original figure.original figure.

The orientation of the image is The orientation of the image is reversed. That is, if triangle ABC reversed. That is, if triangle ABC is read clockwise, then triangle is read clockwise, then triangle A’B’C’ is read counterclockwise.A’B’C’ is read counterclockwise.

Line segments that join matching Line segments that join matching points are parallel. They are points are parallel. They are perpendicular to the reflection perpendicular to the reflection line and bisected by the reflection line and bisected by the reflection line.line.

A triangle with vertices A’(-5,4), B’(-2,1), and C’(-6,-3) is the image of A triangle with vertices A’(-5,4), B’(-2,1), and C’(-6,-3) is the image of

triangle ABC under a reflection in the y-axis.triangle ABC under a reflection in the y-axis.

a)a) Draw a diagram to show the image triangle A’B’C’ and the original Draw a diagram to show the image triangle A’B’C’ and the original triangle ABC.triangle ABC.

b)b) Determine the coordinates of the vertices of triangle ABC.Determine the coordinates of the vertices of triangle ABC.

a) On a coordinate grid draw triangle A’B’C’. The original triangle ABC was reflected in the y-axis to become triangle A’B’C’.

Hence, we can reflect triangle A’B’C’ in the y-axis to return to the original triangle.

Since A’ is 5 units to the left of the y-axis, A must be 5 units to the right of the y-axis.

Similarly, B is 2 units to the right of the y-axis, and C is 6 units to the right of the y-axis.

b) The coordinates of the vertices of triangle ABC are A(5,4), B(2,1), and C(6,-3).

Combining TransformationsCombining Transformations: We can use mapping rules to combine two reflections, or to combine a reflection with a translation.

A polygon has vertices A(1,3), B(3,3), C(3,1), D(5,1), and E(5,5).

a) Graph the polygon and its image, polygon A’B’C’D’E’, under the translation (x,y) (x+4,y+5)

b) On the same grid, graph the image of polygon A’B’C’D’E’ under the reflection (x,y) (-x,y)

a) Draw polygon ABCDE on a coordinate grid.

To apply the mapping rule (x,y) (x+4,y+5), we add up 4 to the x-coordinate and add 5 to the y-coordinate of each vertex of polygon ABCDE.

This moves it 4 units right and 5 units up to become polygon A’B’C’D’E’.

b) To apply the mapping rule (x,y) (-x,y) to the image, we multiply each x-coordinate by -1 and keep the y-coordinate the same.

This reflects the image in the y-axis to become polygon A”B”C”D”E”.

The coordinates of its vertices are A”(-4,8),B”(-6,8),C”(-6,6),D”(-8,6), and E”(-8,10)

Class Work

• Copy Notes to Lesson 29

• Complete Lesson 29 worksheet