Question

graph the image of △def after a reflection over the x-axis.

Explanation:

Step1: Find coordinates of D, E, F

First, identify the coordinates of the vertices of \( \triangle DEF \). From the graph:

• \( D \): Let's see the grid. Moving left/right (x) and up/down (y). \( D \) is at \( (-1, -8) \)? Wait, no, looking at the grid, the x-axis is horizontal, y-axis vertical. Wait, the original points: Let's check the positions. Wait, the y-axis has negative below x-axis. Wait, the point E: looking at the grid, E is at \( (-1, -4) \)? Wait, no, the blue line: D is at \( (-1, -8) \), E is at \( (-1, -4) \), and F is at \( (8, -9) \)? Wait, no, let's re-examine. Wait, the grid: each square is 1 unit. Let's find the coordinates:

• Point D: x = -1, y = -8 (since it's 1 unit left of y-axis, 8 units below x-axis)
• Point E: x = -1, y = -4 (1 unit left of y-axis, 4 units below x-axis)
• Point F: x = 8, y = -9 (8 units right of y-axis, 9 units below x-axis)

Wait, reflection over x-axis: the rule for reflection over x-axis is \( (x, y) \to (x, -y) \). So we take each point, keep x the same, multiply y by -1.

Step2: Apply reflection rule to each point

• For \( D(-1, -8) \): Reflect over x-axis: \( (-1, -(-8)) = (-1, 8) \)
• For \( E(-1, -4) \): Reflect over x-axis: \( (-1, -(-4)) = (-1, 4) \)
• For \( F(8, -9) \): Reflect over x-axis: \( (8, -(-9)) = (8, 9) \)

Step3: Plot the reflected points

Now, plot the new points \( D'(-1, 8) \), \( E'(-1, 4) \), and \( F'(8, 9) \), then connect them to form the reflected triangle.

Answer:

The reflected triangle \( \triangle D'E'F' \) has vertices at \( D'(-1, 8) \), \( E'(-1, 4) \), and \( F'(8, 9) \). (To graph, plot these points and connect them.)