7 4 Translations and Vectors Geometry Translation A

Translation A translation is a transformation that maps all points to new points so

Translation Sketch a triangle with vertices A(-1, -3), B(1, -1), and C(-1, 0). Then

TRANSLATION Sketch a parallelogram with vertices R(-4, -1), S(-2, 0), T(-1, 3), U(-3, 2).

Translation Triangle ABC Triangle A’B’C’ by a translation defined by (x, y) (x –

Vectors A vector is a quantity that has both direction and magnitude (size), and

Vector • Initial Point – Starting Point • Terminal Point – Ending Point Naming

Component Form The component form of a vector combines the horizontal and vertical components.

Identifying Vector Components The initial point of a vector is V(-2, 3) and the

Identifying Vector Components The initial point of a vector is E(2, -6) and the

Translation Using Vectors The component form of vector RS is <2, -3>. Use vector

Translation Using Vectors The component form of vector MN is <3, 1>. Use vector

Translation Using Vectors The component form of GH is <4, 2>. Use GH to

Finding Vectors In the diagram, ABC maps onto A’B’C’ by a translation. Write the

Finding Vectors In the diagram, EFGH maps onto E’F’G’H’ by a translation. Write the

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7. 4 Translations and Vectors Geometry

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.

Translation

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)

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)

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’?

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

Vector • Initial Point – Starting Point • Terminal Point – Ending Point Naming a vector

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

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.

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.

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).

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).

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).

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.

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.

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.