2019 AMC 10A Problem 8
Problem 8 of 25EasierGeometry
The figure below shows line with a regular, infinite, recurring pattern of squares and line segments.
How many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into itself?
• some rotation around a point of line
• some translation in the direction parallel to line
• the reflection across line
• some reflection across a line perpendicular to line
How many of the following four kinds of rigid motion transformations of the plane in which this figure is drawn, other than the identity transformation, will transform this figure into itself?
• some rotation around a point of line
• some translation in the direction parallel to line
• the reflection across line
• some reflection across a line perpendicular to line Answer choices
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Solution
The first transformation works, as we can rotate around the midpoint between an upward-facing and downward-facing square.
The second also works, as we can just move to the right until the squares line up with each other again.
The third fails, as a reflection would cause the line segments to face the opposite direction.
The fourth transformation also doesn’t work since the diagonal lines would again be facing in the wrong direction.
Thus, C is the correct answer.