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 assume the grid. Looking at the graph, \( D \) is at \( (2, -7) \)? Wait, no, looking again. Wait, the y-axis: the points. Wait, F is at (-3, -3)? Wait, no, let's check the grid. Wait, the x-axis is horizontal, y-axis vertical. Let's find each point:

Wait, F: x=-3, y=-3? Wait, no, the blue points: F is at (-3, -3)? Wait, D: let's see, D is at (2, -7)? Wait, no, the graph: the vertical lines are x from -10 to 10, horizontal y from -10 to 10. Let's check the coordinates:

Looking at F: x=-3, y=-3? Wait, no, the line from F to D to E. Wait, F is at (-3, -3)? Wait, D is at (2, -7)? Wait, E is at (6, -7)? Wait, maybe I misread. Wait, let's check again. Wait, the y-coordinate for D and E: they are on the same horizontal line, so same y. Let's see, the grid: each square is 1 unit. So F: x=-3, y=-3? Wait, no, the blue triangle: F is at (-3, -3), D is at (2, -7), E is at (6, -7)? Wait, no, the y-axis: the numbers are -10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10. So D is at (2, -7)? Wait, no, the vertical line for x=2, and y=-7? Wait, the horizontal line for y=-7: D and E are on y=-7. So D is (2, -7), E is (6, -7), F is (-3, -3). Wait, maybe.

Wait, reflection over x-axis: the rule is \( (x, y)
ightarrow (x, -y) \). So for each point, we change the sign of the y-coordinate.

Step2: Apply reflection rule to each point

• For point \( D \): Let's confirm coordinates. Wait, looking at the graph, D is at (2, -7)? Wait, no, the y-axis: the grid lines. Let's count: from x=0, moving right 2 units: x=2. From y=0, moving down 7 units: y=-7. So D(2, -7). Reflection over x-axis: \( (2, -7)

ightarrow (2, 7) \)? Wait, no: reflection over x-axis is (x, y) → (x, -y). So if y is -7, then -y is 7. So D' is (2, 7).

• For point \( E \): E is at (6, -7). Reflection: \( (6, -7)

ightarrow (6, 7) \).

• For point \( F \): F is at (-3, -3). Reflection: \( (-3, -3)

ightarrow (-3, 3) \).

Step3: Plot the reflected points

Now, plot the points \( D'(2, 7) \), \( E'(6, 7) \), and \( F'(-3, 3) \), then connect them to form the reflected triangle \( \triangle D'E'F' \).

Answer:

The image of \( \triangle DEF \) after reflection over the x - axis has vertices at \( D'(2, 7) \), \( E'(6, 7) \), and \( F'(-3, 3) \). (To graph, plot these points and connect them.)