Question

Pentagon PQRST and its reflection, pentagon P′Q′R′S′T′, are shown in the coordinate plane below:

Pentagon PQRST and pentagon P prime Q prime R prime S prime T prime on the coordinate plane with ordered pairs at P negative 4, 6, at Q negative 7, 4, at R negative 6, 1, at S negative 2, 1, at T negative 1, 4, at P prime negative 4, negative 6, at Q prime negative 7, negative 4, at R prime negative 6, negative 1, at S prime negative 2, negative 1, at T prime negative 1, negative 4

What is the line of reflection between pentagons PQRST and P′Q′R′S′T′?
x = 1
y = x
x = 0
y = 0

Answer 1

To determine the line of reflection between pentagons PQRST and P′Q′R′S′T′, we can analyze how the coordinates of the points in pentagon PQRST relate to those in pentagon P′Q′R′S′T′.

The coordinates of pentagon PQRST are:
- \( P(-4, 6) \)
- \( Q(-7, 4) \)
- \( R(-6, 1) \)
- \( S(-2, 1) \)
- \( T(-1, 4) \)

The coordinates of pentagon P′Q′R′S′T′ are:
- \( P'(-4, -6) \)
- \( Q'(-7, -4) \)
- \( R'(-6, -1) \)
- \( S'(-2, -1) \)
- \( T'(-1, -4) \)

Observing the y-coordinates of the points in PQRST and P′Q′R′S′T′ shows that each point has its y-coordinate reflected across the x-axis (the line \(y = 0\)). Specifically, for each point \((x, y)\) in PQRST, the corresponding point in P′Q′R′S′T′ is \((x, -y)\).

Thus, the line of reflection between the two pentagons is the x-axis, which is represented by the equation:

**y = 0**.

Therefore, the correct answer is **y = 0**.