Question

graph the image of △abc after a translation 1 unit left and 6 units up.

Explanation:

Step1: Find coordinates of A, B, C

From the graph:

• \( A(-6, 1) \)
• \( B(-6, 3) \)
• \( C(0, -1) \)

Step2: Apply translation (left 1, up 6)

Translation rule: \((x, y) \to (x - 1, y + 6)\)

• For \( A(-6, 1) \):

\( x' = -6 - 1 = -7 \), \( y' = 1 + 6 = 7 \) → \( A'(-7, 7) \)

• For \( B(-6, 3) \):

\( x' = -6 - 1 = -7 \), \( y' = 3 + 6 = 9 \) → \( B'(-7, 9) \)

• For \( C(0, -1) \):

\( x' = 0 - 1 = -1 \), \( y' = -1 + 6 = 5 \) → \( C'(-1, 5) \)

Step3: Plot \( A' \), \( B' \), \( C' \)

Plot the new points \( (-7, 7) \), \( (-7, 9) \), \( (-1, 5) \) and connect them to form \( \triangle A'B'C' \).

(Note: Since the task is to graph, the final answer involves plotting these points. The coordinates of the translated triangle are \( A'(-7, 7) \), \( B'(-7, 9) \), \( C'(-1, 5) \).)

Answer:

Step1: Find coordinates of A, B, C

From the graph:

• \( A(-6, 1) \)
• \( B(-6, 3) \)
• \( C(0, -1) \)

Step2: Apply translation (left 1, up 6)

Translation rule: \((x, y) \to (x - 1, y + 6)\)

• For \( A(-6, 1) \):

\( x' = -6 - 1 = -7 \), \( y' = 1 + 6 = 7 \) → \( A'(-7, 7) \)

• For \( B(-6, 3) \):

\( x' = -6 - 1 = -7 \), \( y' = 3 + 6 = 9 \) → \( B'(-7, 9) \)

• For \( C(0, -1) \):

\( x' = 0 - 1 = -1 \), \( y' = -1 + 6 = 5 \) → \( C'(-1, 5) \)

Step3: Plot \( A' \), \( B' \), \( C' \)

Plot the new points \( (-7, 7) \), \( (-7, 9) \), \( (-1, 5) \) and connect them to form \( \triangle A'B'C' \).

(Note: Since the task is to graph, the final answer involves plotting these points. The coordinates of the translated triangle are \( A'(-7, 7) \), \( B'(-7, 9) \), \( C'(-1, 5) \).)