Question

write the coordinates of the vertices after a reflection over the x-axis.

Explanation:

Step1: Find original coordinates

First, identify the original coordinates of points \( B \), \( C \), and \( D \) from the graph.

• For point \( B \): Looking at the grid, it is at \( (-2, -2) \).
• For point \( C \): It is at \( (5, -2) \) (wait, no, looking again, the x-coordinate for \( C \) seems to be 4? Wait, the grid: each square is 1 unit. Let's check again. The x-axis: from -10 to 10, each grid line is 1. So \( B \) is at \( x = -2 \), \( y = -2 \). \( C \) is at \( x = 5 \)? Wait, no, the horizontal line from \( B \) to \( C \): \( B \) is at \( (-2, -2) \), \( C \) is at \( (4, -2) \)? Wait, the graph: the x-coordinate for \( C \) is 4? Wait, the grid: let's count. From \( x = -2 \) (B) to \( C \): moving right 6 units? Wait, no, the grid lines: each square is 1. So \( B \) is at \( (-2, -2) \), \( C \) is at \( (4, -2) \), and \( D \) is at \( (-6, -7) \)? Wait, no, the y-coordinate for \( D \): looking at the grid, \( D \) is at \( y = -7 \)? Wait, no, the vertical axis: from -10 to 10. Let's re-express:

Wait, the original points:

• \( B \): \( x = -2 \), \( y = -2 \) (since it's on the line \( y = -2 \), x=-2)
• \( C \): \( x = 4 \), \( y = -2 \) (since it's on the line \( y = -2 \), x=4)
• \( D \): \( x = -6 \), \( y = -7 \) (looking at the grid, D is at x=-6, y=-7)

Step2: Apply reflection over x-axis

The rule for reflecting a point \( (x, y) \) over the x-axis is \( (x, -y) \).

• For \( B(-2, -2) \):

Apply the rule: \( x = -2 \), \( y = -2 \), so new \( y \)-coordinate is \( -(-2) = 2 \). Thus, \( B'(-2, 2) \).

• For \( C(4, -2) \):

Apply the rule: \( x = 4 \), \( y = -2 \), so new \( y \)-coordinate is \( -(-2) = 2 \). Thus, \( C'(4, 2) \).

• For \( D(-6, -7) \):

Apply the rule: \( x = -6 \), \( y = -7 \), so new \( y \)-coordinate is \( -(-7) = 7 \). Thus, \( D'(-6, 7) \).

Answer:

\( B'(-2, 2) \)
\( C'(4, 2) \)
\( D'(-6, 7) \)