Question

find the coordinates of the vertices after the reflection over the line.

\\(g = (\quad, \quad)\\)
\\(h = (\quad, \quad)\\)
\\(e = (\quad, \quad)\\)
\\(f = (\quad, \quad)\\)

Explanation:

⚡ Using what you learned: reflections

Step 1: Identify original coordinates and the line of reflection

Identify the coordinates of the vertices from the graph:

• \( E = (-3, 3) \)
• \( F = (5, 3) \)
• \( G = (5, -3) \)
• \( H = (-3, -3) \)

The dashed line of reflection \( k \) passes through points like \( (0, -5) \), \( (5, 0) \), and \( (9, 4) \).
The equation of this line is:

$$ y = x - 5 $$

Step 2: Apply reflection rule

For a reflection across a line \( y = x - c \), the mapping rule is:

$$ (x, y) ightarrow (y + c, x - c) $$

Here, \( c = 5 \), so the rule is:

$$ (x, y) ightarrow (y + 5, x - 5) $$

Applying this to each vertex:

• For \( G(5, -3) \):

$$ G' = (-3 + 5, 5 - 5) = (2, 0) $$

• For \( H(-3, -3) \):

$$ H' = (-3 + 5, -3 - 5) = (2, -8) $$

• For \( E(-3, 3) \):

$$ E' = (3 + 5, -3 - 5) = (8, -8) $$

• For \( F(5, 3) \):

$$ F' = (3 + 5, 5 - 5) = (8, 0) $$

Answer:

• \( G' = (2, 0) \)
• \( H' = (2, -8) \)
• \( E' = (8, -8) \)
• \( F' = (8, 0) \)