Translations Identifying Translation Tell whether this transformation appears

Identifying Translation • Tell whether this transformation appears to be a translation. Explain.

Definition • A translation is a transformation where all the points of a figure

Drawing Translations • Copy the triangle and the translation vector. Draw the translation of

Definition • Hence we now know that a translation is a transformation along a

Translations in the Coordinate Plane • Horizontal Translation along Vector ‹a, 0›. y •

Translations in the Coordinate Plane • Vertical Translation along Vector ‹ 0, b›. •

Translations in the Coordinate Plane • General Translation along Vector ‹a, b›. • P’(x

Example • Translate the triangle with vertices A(– 2, – 4), B(– 1, –

Assessment • 1. Is this transformation a translation? • Explain. No, This is not

2. Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1, – 1) and

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Translations

Identifying Translation • Tell whether this transformation appears to be a translation. Explain.

Definition • A translation is a transformation where all the points of a figure are moved the same distance in the same direction. • A transformation is an isometry, so the image of a translated figure is congruent to the pre-image.

Activity

Drawing Translations • Copy the triangle and the translation vector. Draw the translation of the triangle along.

Drawing Translations

Definition • Hence we now know that a translation is a transformation along a vector such that each segment joining a point and its image has the same length as the vector and is parallel to the vector.

Translations in the Coordinate Plane • Horizontal Translation along Vector ‹a, 0›. y • P(x, y) P’(x + a, y) 0 • (x, y) (x + a, y) x

Translations in the Coordinate Plane • Vertical Translation along Vector ‹ 0, b›. • P’ (x, y + b) P (x , y) • 0 • (x, y) (x, y + b) y x

Translations in the Coordinate Plane • General Translation along Vector ‹a, b›. • P’(x + a, y + b) y • • P(x , y) 0 • (x, y) (x + a, y + b) x

Example • Translate the triangle with vertices A(– 2, – 4), B(– 1, – 2) and C(– 3, 0) along the vector (2, 4). The image of (x, y) is (x + 2, y + 4). A(– 2, – 4) A’(– 2 + 2, – 4 + 4) = A’(0, 0) B(– 1, – 2) B’(– 1 + 2, – 2 + 4) = B’(1, 2) C C(– 3, 0) C’(– 3 + 2, 0 + 4) = C’(– 1, 4) B A Answers

Assessment • 1. Is this transformation a translation? • Explain. No, This is not a Translation because the two objects are not congruent Answer

2. Translate the quadrilateral with vertices R(2, 5), S(0, 2), T(1, – 1) and U(3, 1) along the vector ‹– 3, – 3›. R(2, 5) R’ (– 1, 2) S(0, 2) S’ (– 3, – 1) T(1, – 1) T’ (– 2, – 4) U(3, 1) U’ (0, – 2) Answer

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