Question

reflect the figure across the x-axis. then decide if

Explanation:

Step1: Identify original vertices

First, find the coordinates of the vertices of the original trapezoid. Let's assume the vertices (from the graph) are: \( A(-8, -4) \), \( B(-4, -4) \), \( C(-3, -6) \), \( D(-9, -6) \) (we determine these by looking at the grid, each square is 1 unit).

Step2: Apply reflection over x - axis

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

• For point \( A(-8, -4) \): After reflection, \( A'(-8, 4) \) (since \( y=-4\), so \(-y = 4\))
• For point \( B(-4, -4) \): After reflection, \( B'(-4, 4) \)
• For point \( C(-3, -6) \): After reflection, \( C'(-3, 6) \)
• For point \( D(-9, -6) \): After reflection, \( D'(-9, 6) \)

Step3: Plot the reflected points

Plot the points \( A'(-8, 4) \), \( B'(-4, 4) \), \( C'(-3, 6) \), \( D'(-9, 6) \) on the coordinate plane and connect them to get the reflected figure.

(Note: If the question was also about congruence or something else, after reflection, the figure is congruent to the original because reflection is a rigid transformation that preserves side lengths and angles. But since the original question was cut off, but the main task was reflection, the reflection steps are as above.)

Answer:

To reflect the figure across the \(x\) - axis, use the rule \((x,y)\to(x, -y)\) for each vertex. If the original vertices are \( A(-8, -4) \), \( B(-4, -4) \), \( C(-3, -6) \), \( D(-9, -6) \), the reflected vertices are \( A'(-8, 4) \), \( B'(-4, 4) \), \( C'(-3, 6) \), \( D'(-9, 6) \). Plot these points to get the reflected figure.