Question

reflect the triangle abc by the blue line.
write the coordinate of the triangle abc and the coordinate of the reflection of abc by the blue line.
a (..., ...)
b (..., ...)
c (..., ...)
the reflection of abc is abc. the coordinates are:
a (..., ...)
b (..., ...)
c (..., ...)

Explanation:

Step1: Determine coordinates of ABC

From the graph, assume the blue line is \( x = 0 \) (y - axis) for reflection. Let's find coordinates:

• \( A \): Looking at the right graph, \( A \) is at \( (2, 1) \) (x = 2, y = 1).
• \( B \): \( B \) is at \( (6, 2) \) (x = 6, y = 2).
• \( C \): \( C \) is at \( (6, 5) \) (x = 6, y = 5).

Step2: Reflect over y - axis (\( x = 0 \))

The rule for reflection over y - axis is \( (x,y)\to(-x,y) \).

• For \( A(2,1) \): Apply rule, \( A'(-2,1) \).
• For \( B(6,2) \): Apply rule, \( B'(-6,2) \).
• For \( C(6,5) \): Apply rule, \( C'(-6,5) \).

Answer:

Coordinates of \( \triangle ABC \):
\( A(2, 1) \)
\( B(6, 2) \)
\( C(6, 5) \)

Coordinates of \( \triangle A'B'C' \) (reflection):
\( A'(-2, 1) \)
\( B'(-6, 2) \)
\( C'(-6, 5) \)