1. 7.4 Translations and Vectors
Advanced Geometry

2. Translation
A translation is a transformation that maps all points to new points so that the distance from every old point to every new corresponding point is equal.

3. Translation

4. Translation
Sketch a triangle with vertices A(-1, -3), B(1, -1), and C(-1, 0). Then sketch the image of the triangle after the translation… (x, y)  (x – 3, y + 4) The translation above is in coordinate notation

6. TRANSLATION
Sketch a parallelogram with vertices R(-4,-1), S(-2,0), T(-1,3), U(-3,2). Then sketch the image of the parallelogram after translation… (x,y)  (x + 4, y – 2)

8. Translation
Triangle ABC  Triangle A’B’C’ by a translation defined by (x, y)  (x – 5, y). The coordinates of the vertices of triangle ABC are A(7, 4), B(-1, -1), and C(3, -5). What are the coordinates of the vertices of triangle A’B’C’?

10. Vectors
A vector is a quantity that has both direction and magnitude (size), and is represented by an arrow drawn between two points.

11. Component Form
The component form of a vector combines the horizontal and vertical components. Let’s take a look at an example….

13. Identifying Vector Components
The initial point of a vector is V(-2, 3) and the terminal point is W(-4, -7). Name the vector and write its component parts.

14. Identifying Vector Components
The initial point of a vector is E(2, -6) and the terminal point is F(2, -9). Name the vector and write its component parts.

15. Translation Using Vectors
The component form of vector RS is <2,-3>. Use vector RS to translate the quadrilateral whose vertices are G(-3,5), H(0,3), J(1,3), and K(3,-2).

17. Translation Using Vectors
The component form of vector MN is <3,1>. Use vector MN to translate the triangle whose vertices are R(0,4), S(3,1), and T(4,-2).

19. Translation Using Vectors
The component form of GH is <4, 2>. Use GH to translate the triangle whose vertices are (3, -1), B(1, 1), and C(3, 5).

20. Finding Vectors
In the diagram, ABC maps onto A’B’C’ by a translation. Write the component form of the vector that can be used to describe the translation.

21. Finding Vectors
In the diagram, EFGH maps onto E’F’G’H’ by a translation. Write the component form of the vector that can be used to describe the translation.

22. Finding Vectors
In the diagram, ABC maps onto A’B’C’ by a translation. Write the component form of the vector that can be used to describe the translation.

23. Using Vectors
The coordinates of a logging site are S(5, 7). A logging truck traveling a straight line from the site to a mill at M encounters a road detour at D when it is 4 mi west and 2 mi south of the logging site. The truck must travel an alternate route to A(4, 3).
Write the component forms of the vectors from S to D and from D to A.
The mill is 6 mi west and 3 mi south of the logging site. Write the component form of the vector that describes the route the logging truck can follow to arrive at the mill.