Question

write the coordinates of the vertices after a reflection over the y - axis.
a((□,□))
b((□,□))
c((□,□))
d((□,□))

Explanation:

Step1: Find original coordinates

From the graph:

• \( A(-10, -10) \)
• \( B(0, -10) \)
• \( C(0, -1) \) (Wait, correction: Looking at the grid, \( C \) is at \( (0, -1) \)? No, recheck: The y-axis at \( x=0 \), \( C \) is at \( (0, -1) \)? Wait, no, the red square: \( A \) is at \( (-10, -10) \), \( D \) at \( (-10, -1) \)? Wait, no, the grid lines: Let's re-express.

Wait, the original vertices:

• \( A \): x=-10, y=-10 (since it's at the intersection of x=-10 and y=-10)
• \( B \): x=0, y=-10 (on y-axis, y=-10)
• \( C \): x=0, y=-1 (on y-axis, y=-1? Wait, no, the red line from \( C \) to \( B \) is vertical. Wait, the grid: each square is 1 unit. So \( C \) is at \( (0, -1) \)? No, looking at the y-axis labels: the bottom is -10, then -8, -6, -4, -2, 0, 2, etc. Wait, the red square: \( A \) is at (-10, -10), \( B \) at (0, -10), \( C \) at (0, -1), \( D \) at (-10, -1). Wait, no, the vertical line from \( C \) to \( B \): from y=-1 to y=-10? No, the arrow at the bottom is -10, so \( B \) is at (0, -10), \( C \) is at (0, -1) (since the distance from \( C \) to \( B \) is 9 units? No, maybe I misread. Wait, the original figure: \( A \) is at (-10, -10), \( D \) at (-10, -1), \( C \) at (0, -1), \( B \) at (0, -10). Yes, that makes a rectangle.

Step2: Reflection over y-axis rule

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

Step3: Reflect each vertex

• For \( A(-10, -10) \): Apply \( (-x, y) \) → \( (10, -10) \) (so \( A' = (10, -10) \))
• For \( B(0, -10) \): \( x=0 \), so \( (-0, -10) = (0, -10) \) ( \( B' = (0, -10) \) )
• For \( C(0, -1) \): \( x=0 \), so \( (-0, -1) = (0, -1) \) ( \( C' = (0, -1) \) )
• For \( D(-10, -1) \): Apply \( (-x, y) \) → \( (10, -1) \) ( \( D' = (10, -1) \) )

Wait, correction: Wait, original \( D \): looking at the graph, \( D \) is at (-10, -1) (since it's on x=-10, y=-1), \( A \) at (-10, -10), \( B \) at (0, -10), \( C \) at (0, -1). So reflection over y-axis:

• \( A(-10, -10) \) → \( (10, -10) \) (A')
• \( B(0, -10) \) → \( (0, -10) \) (B') (since x=0, reflection doesn't change it)
• \( C(0, -1) \) → \( (0, -1) \) (C') (x=0, no change)
• \( D(-10, -1) \) → \( (10, -1) \) (D')

Answer:

\( A'(10, -10) \), \( B'(0, -10) \), \( C'(0, -1) \), \( D'(10, -1) \)

(Note: If original coordinates were misread, adjust. But based on the grid, \( A(-10, -10) \), \( B(0, -10) \), \( C(0, -1) \), \( D(-10, -1) \) is correct. Reflection over y-axis flips the x-coordinate's sign, so negative x becomes positive, positive x (or 0) stays.)