Question

translate △abc using the rule (x, y) → (x + 6, y - 3) to form △abc. what are the coordinates of abc? a( , ) a( , ) b( , ) b( , ) c( , ) c( , )

Explanation:

Step1: Determine coordinates of A, B, C

From the grid, assume:

• \( A \) is at \( (2, 3) \) (since it's 2 units right on x, 3 up on y)
• \( B \) is at \( (-2, -1) \) (2 units left on x, 1 down on y)
• \( C \) is at \( (-1, 4) \) (1 unit left on x, 4 up on y)

Step2: Apply translation rule \((x, y) \to (x + 6, y - 3)\) to A

For \( A(2, 3) \):
\( x' = 2 + 6 = 8 \)
\( y' = 3 - 3 = 0 \)
So \( A'(8, 0) \)

Step3: Apply translation rule to B

For \( B(-2, -1) \):
\( x' = -2 + 6 = 4 \)
\( y' = -1 - 3 = -4 \)
So \( B'(4, -4) \)

Step4: Apply translation rule to C

For \( C(-1, 4) \):
\( x' = -1 + 6 = 5 \)
\( y' = 4 - 3 = 1 \)
So \( C'(5, 1) \)

Answer:

• \( A(2, 3) \), \( A'(8, 0) \)
• \( B(-2, -1) \), \( B'(4, -4) \)
• \( C(-1, 4) \), \( C'(5, 1) \)