Question

1. triangle abc is translated 4 units to the left and 5 units up to form triangle abc.

image of a coordinate grid with triangle abc
what are the coordinates of the vertices of figure abc?
label the vertices with the correct ordered pairs.

Explanation:

Step1: Find original coordinates

First, identify the coordinates of \( A \), \( B \), and \( C \) from the graph.

• \( A \) is at \( (1, 2) \)
• \( B \) is at \( (3, 6) \)
• \( C \) is at \( (8, 2) \)

Step2: Apply translation (left 4, up 5)

For a translation 4 units left (subtract 4 from \( x \)-coordinate) and 5 units up (add 5 to \( y \)-coordinate):

• For \( A(1, 2) \):

New \( x \): \( 1 - 4 = -3 \)
New \( y \): \( 2 + 5 = 7 \)
So \( A'(-3, 7) \)

• For \( B(3, 6) \):

New \( x \): \( 3 - 4 = -1 \)
New \( y \): \( 6 + 5 = 11 \)
So \( B'(-1, 11) \)

• For \( C(8, 2) \):

New \( x \): \( 8 - 4 = 4 \)
New \( y \): \( 2 + 5 = 7 \)
So \( C'(4, 7) \)

Answer:

\( A'(-3, 7) \), \( B'(-1, 11) \), \( C'(4, 7) \)