EXAMPLE 3 Identify vector components Name the vector and write its component form. SOLUTION The vector is BC. From initial point B to terminal point C, you move 9 units right and 2 units down. So, the component form is 9, –2. a.

EXAMPLE 3 Name the vector and write its component form. Identify vector components b. The vector is ST. From initial point S to terminal point T, you move 8 units left and 0 units vertically. The component form is –8, 0. SOLUTION

EXAMPLE 4 Use a vector to translate a figure The vertices of ∆ABC are A (0, 3), B (2, 4), and C (1, 0). Translate ∆ABC using the vector 5, –1. SOLUTION First, graph ∆ABC. Use 5, –1 to move each vertex 5 units to the right and 1 unit down. Label the image vertices. Draw ∆ A′B′C′. Notice that the vectors drawn from preimage to image vertices are parallel.

GUIDED PRACTICE for Examples 3 and 4 4. Name the vector and write its component form. The vector is RS. From initial point R to terminal point S, you move 5 units right and 0 units vertically. The component form is 5, 0. SOLUTION

GUIDED PRACTICE for Examples 3 and 4 5. Name the vector and write its component form. The vector is TX. From initial point T to terminal point S, you move 0 units horizontally and 3 units up. The component form is 0, 3. SOLUTION

GUIDED PRACTICE for Examples 3 and 4 6. Name the vector and write its component form. SOLUTION The vector is BK. From initial point B to terminal point K, you move 5 units left and 2 units up. So, the component form is –5, 2.

GUIDED PRACTICE for Examples 3 and 4 7. The vertices of ∆LMN are L (2, 2), M (5, 3), and N (9, 1). Translate ∆LMN using the vector –2, 6. SOLUTION Find the translation of each vertex by subtracting 2 from its x -coordinate and adding 6 to its y -coordinate. (x, y) → (x – 2, y + 6) L (2, 2) → L ′(0, 8) M (5, 3) → M ′(3, 9) N (9, 1) → N ′(7, 7)