Question

what is the line of reflection for the trapezoids?

Explanation:

Identify coordinates of corresponding vertices

Identify the coordinates of the original trapezoid \(ABCD\) and its reflected image \(A'B'C'D'\) from the grid:

• \(A(5, 4)\) and \(A'(1, 4)\)
• \(B(6, 4)\) and \(B'(0, 4)\)
• \(C(8, 3)\) and \(C'(-2, 3)\)
• \(D(5, 3)\) and \(D'(1, 3)\)

Calculate the midpoint of corresponding points

The line of reflection is a vertical line perpendicular to the segments connecting corresponding vertices. Calculate the midpoint \(x\)-coordinate for any pair:

$$ x = \frac{x_A + x_{A'}}{2} = \frac{5 + 1}{2} = 3 $$

$$ x = \frac{x_B + x_{B'}}{2} = \frac{6 + 0}{2} = 3 $$

Determine the equation of the line of reflection

Since the \(y\)-coordinates remain unchanged and the midpoints of the \(x\)-coordinates are constantly at \(3\), the line of reflection is the vertical line:

$$ x = 3 $$

Answer:

The line of reflection for the trapezoids is \(x = 3\).