Page 107 - Math Course 2 (Book 2)

Transformations: Using Vectors

Add Vectors
Scalar Multiplication
Example
Words To multiply a vector by a scalar, multiply
each component by the scalar.
Graph the image of ΔEFG with vertices E(1, –3),
Symbols If a = (a , a ) has a magnitude | a | and F(3, –1), and G(4, –4) under the translationand
1 2
direction d, then na = n(a , a ) = a = 〈–4, 2 ⟩ and b = 〈 2, 3 ⟩.
1 2
(na , na ), where n is a positive real
1 2 Graph ΔEFG
number, the magnitude is | na |, and its Method 1: Translate two times.
direction is d.
y Translate ΔEFG by a. Then translate this image of
Model ΔEFG by b.
Translate each a 4 units left and 2 units up.

Then translate each vertex of 2 units right and 3

a na units up. Label the image ΔE'F'G'.
x

Let’s Begin

Translations with Vectors

Example
Method 2: Find the resultant, and then translate.
Add a and b.
Graph the image of quadrilateral HJLK with
vertices H(–4, 4), J(–2, 4), L(–1, 2) and K(–3, 1) a + b = 〈–4 + 2, 2 + 3⟩
under the translation of v = 〈 5, – 5 ⟩
. = 〈–2, 5⟩
First graph quadrilateral HJLK. Translate each vertex 2 units left and 5 units up.

Next translate each vertex by v , 5 units right and 5
units down.

Connect the vertices for quadrilateral H'J'L'K'.

Answer

Notice that the vertices for
Answer the image are the same for
either method.

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