Question

triangle abc is the image of triangle abc after a translation of 7 units to the left and 3 units up. find the coordinates of triangle abc before the translation.

Explanation:

Step1: Identify coordinates of A', B', C'

From the graph, we can see:

• \( A' \) has coordinates \( (2, -5) \) (assuming the grid and axes, x=2, y=-5)
• \( B' \) has coordinates \( (5, -3) \)
• \( C' \) has coordinates \( (1, -3) \)

Step2: Reverse the translation (7 right, 3 down)

To find the original coordinates of \( A, B, C \), we reverse the translation (since \( A'B'C' \) is the image after translating \( ABC \) 7 left and 3 up, so to get back, we translate \( A'B'C' \) 7 right and 3 down).

The translation rule for reversing is: if a point \( (x', y') \) is the image after translating \( (x, y) \) by \( (h, k) \) (here \( h=-7, k = 3 \) for the original translation), then \( x = x' - h \), \( y = y' - k \). So \( h' = 7 \) (right), \( k' = -3 \) (down).

For point A:

\( x = 2 + 7 = 9 \)
\( y = -5 - 3 = -8 \)
So \( A(9, -8) \)

For point B:

\( x = 5 + 7 = 12 \)
\( y = -3 - 3 = -6 \)
So \( B(12, -6) \)

For point C:

\( x = 1 + 7 = 8 \)
\( y = -3 - 3 = -6 \)
So \( C(8, -6) \)

Answer:

Coordinates of \( A(9, -8) \), \( B(12, -6) \), \( C(8, -6) \)