Question

1. for each pair of images, describe the transformation as a translation, reflection, or rotation.
2. the equation y = -1 is graphed on the coordinate plane shown.

a. graph the line perpendicular to y = -1 that passes through (6,4).
b. graph the line parallel to y = -1 that passes through (-4,8).

Explanation:

Step 1: Analyze transformations in part 1

• a) The triangle has been flipped over a line. This is a reflection.
• b) The triangle has been turned around a point. This is a rotation.
• c) The triangle has been flipped over a line. This is a reflection.
• d) The trapezoid has been moved without rotation or reflection. This is a translation.
• e) The trapezoid has been turned around a point. This is a rotation.
• f) The trapezoid has been moved without rotation or reflection. This is a translation.

Step 2: Analyze lines in part 2

• a) The line $y = - 1$ is a horizontal line. A line perpendicular to it is a vertical line. The vertical line passing through $(6,4)$ has the equation $x = 6$. On the coordinate - plane, it is a straight line passing through $x = 6$ and extending infinitely in both the positive and negative $y$ - directions.
• b) A line parallel to $y=-1$ is also a horizontal line. The line parallel to $y = - 1$ passing through $(-4,8)$ has the equation $y = 8$. On the coordinate - plane, it is a straight line passing through $y = 8$ and extending infinitely in both the positive and negative $x$ - directions.

Answer:

1.

• a) Reflection
• b) Rotation
• c) Reflection
• d) Translation
• e) Rotation
• f) Translation

2.

• a) Graph the vertical line $x = 6$.
• b) Graph the horizontal line $y = 8$.