Lesson 8.1Translating Points•To learn how to graph polygons on the graphing calculator•To write list definitions to describe translations of points•To learn to recognize and graph translations on graph paper.

The Dome of the Rock is a famous site in Jerusalem. Built in the 7th Century, it is well know for its beautiful tile work. Flipping or turning a design could create yet another design. We will explore flipping and turning geometric shapes in mathematics.

Translating PointsIn computer

animation, many individual points define each figure. A figure is animated by moving these points around the screen, little by little, through a series of frames.

Figures in Motion In this investigation you will

learn to move a polygon around the coordinate plane. You will first view what happens when you change the y-coordinates of the vertices.

Name the coordinates of the vertices of this triangle.

Enter the x-coordinates of the vertices into L1 and the corresponding y-coordinates into L2. Enter the first coordinate at the end of each list. Graph the triangle by connecting the vertices.

Define lists L3 and L4 asL3 = L1L4 = L2-3

Graph a second triangle using list L3 for the x-coordinate and L4 for the y-coordinate.

Name the coordinates of the new triangle. Tell how the original triangle has moved. How did the coordinates of the vertices

change?

Graph a second triangle usingL3 = L1L4 = L2+2

Name the coordinates of the new triangle. Tell how the original triangle has moved. How did the coordinates of the vertices

change?Repeat with

L3 = L1L4 = L2-1

Write definitions for list L3 and L4 in terms of L1 and L2 to create each of the following graphs.

Name the coordinates of the vertices of this quadrilateral.

Graph the quadrilateral using lists L1 for the x-coordinates of the vertices and lists L2 for the y-coordinates of the vertices.

Define L3 and L4:L3 = L1-3L4 = L4

Graph a second quadrilateral using L3 and L4.

Describe how the original quadrilateral moved.

How did the coordinates of the vertices change?

Define L3 and L4:L3 = L1 +2L4 = L2

Describe how the original quadrilateral moved.How did the coordinates of the vertices

change?Define L3 and L4:

L3 = L1 +2L4 = L2

Describe how the original quadrilateral moved.How did the coordinates of the vertices

change?

Write definitions for list L3 and L4 in terms of L1 and L2 to create each of the following graphs.

Summarize what you have learned about moving a figure around the coordinate plane.

ExampleSketch the image of this figure after a

translation right 4 units and down 3 units.

Translate every point 4 units to the right and 3 units down.